共查询到20条相似文献,搜索用时 654 毫秒
1.
Let
\mathfrak a \mathfrak{a} be an algebraic Lie subalgebra of a simple Lie algebra
\mathfrak g \mathfrak{g} with index
\mathfrak a \mathfrak{a} ≤ rank
\mathfrak g \mathfrak{g} . Let
Y( \mathfrak a ) Y\left( \mathfrak{a} \right) denote the algebra of
\mathfrak a \mathfrak{a} invariant polynomial functions on
\mathfrak a* {\mathfrak{a}^*} . An algebraic slice for
\mathfrak a \mathfrak{a} is an affine subspace η + V with
h ? \mathfrak a* \eta \in {\mathfrak{a}^*} and
V ì \mathfrak a* V \subset {\mathfrak{a}^*} subspace of dimension index
\mathfrak a \mathfrak{a} such that restriction of function induces an isomorphism of
Y( \mathfrak a ) Y\left( \mathfrak{a} \right) onto the algebra R[ η + V] of regular functions on η + V. Slices have been obtained in a number of cases through the construction of an adapted pair ( h, η) in which
h ? \mathfrak a h \in \mathfrak{a} is ad-semisimple, η is a regular element of
\mathfrak a* {\mathfrak{a}^*} which is an eigenvector for h of eigenvalue minus one and V is an h stable complement to
( \text ad \mathfrak a )h \left( {{\text{ad}}\;\mathfrak{a}} \right)\eta in
\mathfrak a* {\mathfrak{a}^*} . The classical case is for
\mathfrak g \mathfrak{g} semisimple [ 16], [ 17]. Yet rather recently many other cases have been provided; for example, if
\mathfrak g \mathfrak{g} is of type A and
\mathfrak a \mathfrak{a} is a “truncated biparabolic” [ 12] or a centralizer [ 13]. In some of these cases (in particular when the biparabolic is a Borel subalgebra) it was found [ 13], [ 14], that η could be taken to be the restriction of a regular nilpotent element in
\mathfrak g \mathfrak{g} . Moreover, this calculation suggested [ 13] how to construct slices outside type A when no adapted pair exists. This article makes a first step in taking these ideas further. Specifically, let
\mathfrak a \mathfrak{a} be a truncated biparabolic of index one. (This only arises if
\mathfrak g \mathfrak{g} is of type A and
\mathfrak a \mathfrak{a} is the derived algebra of a parabolic subalgebra whose Levi factor has just two blocks whose sizes are coprime.) In this
case it is shown that the second member of an adapted pair ( h, η) for
\mathfrak a \mathfrak{a} is the restriction of a particularly carefully chosen regular nilpotent element of
\mathfrak g \mathfrak{g} . A by-product of our analysis is the construction of a map from the set of pairs of coprime integers to the set of all finite
ordered sequences of ±1. 相似文献
2.
Let
( R,\mathfrak m){(R,\mathfrak m)} be a noetherian, local ring with completion [^( R)]{\hat{R}} . We show that R ì [^( R)]{R \subset \hat{R}} satisfies the condition Going up if and only if there exists to every artinian R-module M with
Ann R( M) ì \mathfrak p{{\rm Ann}_R(M) \subset \mathfrak{p}} a submodule U ì M{U \subset M} with
Ann R( U)=\mathfrak p.{{\rm {Ann}}_R(U)=\mathfrak{p}.} This is further equivalent to R being formal catenary, to α( R) = 0 and to
Hd\mathfrakq/\mathfrakp( R/\mathfrak p)=0{H^d_{\mathfrak{q}/\mathfrak{p}}(R/\mathfrak{p})=0} for all prime ideals
\mathfrak p ì \mathfrak q \subsetneq \mathfrak m{\mathfrak{p} \subset \mathfrak{q} \subsetneq \mathfrak{m}} where
d = dim( R/\mathfrak p){d = {\rm {dim}}(R/\mathfrak{p})}. 相似文献
3.
For an Azumaya algebra A with center C of rank n
2 and a unitary involution τ, we study the stability of the unitary SK 1 under reduction. We show that if R = C
τ is a Henselian ring with maximal ideal
\mathfrak m{\mathfrak{m}} and 2 and n are invertible in R then
SK 1( A, t) @ SK 1( A/ \mathfrak m A, overline t){{{\rm SK}_1}(A, \tau) \cong {{\rm SK}_1}(A/ \mathfrak{m} A, overline \tau)}. 相似文献
4.
We investigate splitting number and reaping number for the structure ( ω)
ω
of infinite partitions of ω. We prove that
\mathfrak rd £ non( M), non( N),\mathfrak d{\mathfrak{r}_{d}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N}),\mathfrak{d}} and
\mathfrak sd 3 \mathfrak b{\mathfrak{s}_{d}\geq\mathfrak{b}} . We also show the consistency results ${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})}${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})} and ${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})}${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})} . To prove the consistency
\mathfrak rd < add( M){\mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})} and
\mathfrak sd < cof( M){\mathfrak{s}_{d} < \mathsf{cof}(\mathcal{M})} we introduce new cardinal invariants
\mathfrak rpair{\mathfrak{r}_{pair}} and
\mathfrak spair{\mathfrak{s}_{pair}} . We also study the relation between
\mathfrak rpair, \mathfrak spair{\mathfrak{r}_{pair}, \mathfrak{s}_{pair}} and other cardinal invariants. We show that
cov( M), cov( N) £ \mathfrak rpair £ \mathfrak sd,\mathfrak r{\mathsf{cov}(\mathcal{M}),\mathsf{cov}(\mathcal{N})\leq\mathfrak{r}_{pair}\leq\mathfrak{s}_{d},\mathfrak{r}} and
\mathfrak s £ \mathfrak spair £ non( M), non( N){\mathfrak{s}\leq\mathfrak{s}_{pair}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N})} . 相似文献
5.
Let
U( \mathfrakg,e ) U\left( {\mathfrak{g},e} \right) be the finite W-algebra associated with a nilpotent element e in a complex simple Lie algebra
\mathfrakg = \textLie(G) \mathfrak{g} = {\text{Lie}}(G) and let I be a primitive ideal of the enveloping algebra
U( \mathfrakg ) U\left( \mathfrak{g} \right) whose associated variety equals the Zariski closure of the nilpotent orbit (Ad G) e. Then it is known that
I = \textAn\textnU( \mathfrakg )( Qe ?U( \mathfrakg,e )V ) I = {\text{An}}{{\text{n}}_{U\left( \mathfrak{g} \right)}}\left( {{Q_e}{ \otimes_{U\left( {\mathfrak{g},e} \right)}}V} \right) for some finite dimensional irreducible
U( \mathfrakg,e ) U\left( {\mathfrak{g},e} \right) -module V, where Q
e
stands for the generalised Gelfand–Graev
\mathfrakg \mathfrak{g} -module associated with e. The main goal of this paper is to prove that the Goldie rank of the primitive quotient
U( \mathfrakg ) | / |
I {{{U\left( \mathfrak{g} \right)}} \left/ {I} \right.} always divides dim V. For
\mathfrakg = \mathfraks\mathfrakln \mathfrak{g} = \mathfrak{s}{\mathfrak{l}_n} , we use a theorem of Joseph on Goldie fields of primitive quotients of
U( \mathfrakg ) U\left( \mathfrak{g} \right) to establish the equality
\textrk( U( \mathfrakg ) | / |
I ) = dimV {\text{rk}}\left( {{{{U\left( \mathfrak{g} \right)}} \left/ {I} \right.}} \right) = \dim V . We show that this equality continues to hold for
\mathfrakg \ncong \mathfraks\mathfrakln \mathfrak{g} \ncong \mathfrak{s}{\mathfrak{l}_n} provided that the Goldie field of
U( \mathfrakg ) | / |
I {{{U\left( \mathfrak{g} \right)}} \left/ {I} \right.} is isomorphic to a Weyl skew-field and use this result to disprove Joseph’s version of the Gelfand–Kirillov conjecture formulated
in the mid-1970s. 相似文献
6.
Let G be a reductive algebraic group over an algebraically closed field K of characteristic zero. Let
p:\mathfrak gr ? X = \mathfrak gr// G \pi :{\mathfrak{g}^r} \to X = {\mathfrak{g}^r}//G be the categorical quotient where
\mathfrak g \mathfrak{g} is the adjoint representation of G and r is a suitably large integer (in general r ≥ 5, but for many cases r ≥ 3 or even r ≥ 2 suffices). We show that every automorphism φ of X lifts to a map
F:\mathfrak gr ? \mathfrak gr \Phi :{\mathfrak{g}^r} \to {\mathfrak{g}^r} commuting with π. As an application we consider the action of φ on the Luna stratification of X. 相似文献
7.
We provide a characterization of the Banach spaces X with a Schauder basis ( e
n
)
n∈ℕ which have the property that the dual space X* is naturally isomorphic to the space L
diag( X) of diagonal operators with respect to ( e
n
)
n∈ℕ. We also construct a Hereditarily Indecomposable Banach space $
\mathfrak{X}
$
\mathfrak{X}
D with a Schauder basis ( e
n
)
n∈ℕ such that $
\mathfrak{X}
$
\mathfrak{X}
* D is isometric to L
diag($
\mathfrak{X}
$
\mathfrak{X}
D) with these Banach algebras being Hereditarily Indecomposable. Finally, we show that every T ∈ L
diag($
\mathfrak{X}
$
\mathfrak{X}
D) is of the form T = λI + K, where K is a compact operator. 相似文献
9.
Let ${\mathfrak{g}}Let
\mathfrakg{\mathfrak{g}} be a finite dimensional simple Lie algebra over an algebraically closed field
\mathbbK\mathbb{K} of characteristic 0. Let
\mathfrakg\mathbbZ{\mathfrak{g}}_{{\mathbb{Z}}} be a Chevalley ℤ-form of
\mathfrakg{\mathfrak{g}} and
\mathfrakg\Bbbk=\mathfrakg\mathbbZ?\mathbbZ\Bbbk{\mathfrak{g}}_{\Bbbk}={\mathfrak{g}}_{{\mathbb{Z}}}\otimes _{{\mathbb{Z}}}\Bbbk, where
\Bbbk\Bbbk is the algebraic closure of
\mathbbFp{\mathbb{F}}_{p}. Let
G\BbbkG_{\Bbbk} be a simple, simply connected algebraic
\Bbbk\Bbbk-group with
\operatornameLie(G\Bbbk)=\mathfrakg\Bbbk\operatorname{Lie}(G_{\Bbbk})={\mathfrak{g}}_{\Bbbk}. In this paper, we apply recent results of Rudolf Tange on the fraction field of the centre of the universal enveloping algebra
U(\mathfrakg\Bbbk)U({\mathfrak{g}}_{\Bbbk}) to show that if the Gelfand–Kirillov conjecture (from 1966) holds for
\mathfrakg{\mathfrak{g}}, then for all p≫0 the field of rational functions
\Bbbk (\mathfrakg\Bbbk)\Bbbk ({\mathfrak{g}}_{\Bbbk}) is purely transcendental over its subfield
\Bbbk(\mathfrakg\Bbbk)G\Bbbk\Bbbk({\mathfrak{g}}_{\Bbbk})^{G_{\Bbbk}}. Very recently, it was proved by Colliot-Thélène, Kunyavskiĭ, Popov, and Reichstein that the field of rational functions
\mathbbK(\mathfrakg){\mathbb{K}}({\mathfrak{g}}) is not purely transcendental over its subfield
\mathbbK(\mathfrakg)\mathfrakg{\mathbb{K}}({\mathfrak{g}})^{\mathfrak{g}} if
\mathfrakg{\mathfrak{g}} is of type B
n
, n≥3, D
n
, n≥4, E6, E7, E8 or F4. We prove a modular version of this result (valid for p≫0) and use it to show that, in characteristic 0, the Gelfand–Kirillov conjecture fails for the simple Lie algebras of the
above types. In other words, if
\mathfrakg{\mathfrak{g}} is of type B
n
, n≥3, D
n
, n≥4, E6, E7, E8 or F4, then the Lie field of
\mathfrakg{\mathfrak{g}} is more complicated than expected. 相似文献
10.
Let R be a noetherian ring,
\mathfrak a{\mathfrak{a}} an ideal of R, and M an R-module. We prove that for a finite module M, if
H i\mathfraka( M){{\rm H}^{i}_{\mathfrak{a}}(M)} is minimax for all i ≥ r ≥ 1, then
H i\mathfraka( M){{\rm H}^{i}_{\mathfrak{a}}(M)} is artinian for i ≥ r. A local–global principle for minimax local cohomology modules is shown. If
H i\mathfraka( M){{\rm H}^{i}_{\mathfrak{a}}(M)} is coatomic for i ≤ r ( M finite) then
H i\mathfraka( M){{\rm H}^{i}_{\mathfrak{a}}(M)} is finite for i ≤ r. We give conditions for a module which is locally minimax to be a minimax module. A non-vanishing theorem and some vanishing
theorems are proved for local cohomology modules. 相似文献
11.
Let
\mathfrak g \mathfrak{g} be a reductive Lie algebra and
\mathfrak k ì \mathfrak g \mathfrak{k} \subset \mathfrak{g} be a reductive in
\mathfrak g \mathfrak{g} subalgebra. A (
\mathfrak g,\mathfrak k \mathfrak{g},\mathfrak{k} )-module M is a
\mathfrak g \mathfrak{g} -module for which any element m ∈ M is contained in a finite-dimensional
\mathfrak k \mathfrak{k} -submodule of M. We say that a (
\mathfrak g,\mathfrak k \mathfrak{g},\mathfrak{k} )-module M is bounded if there exists a constant C
M
such that the Jordan-H?lder multiplicities of any simple finite-dimensional
\mathfrak k \mathfrak{k} -module in every finite-dimensional
\mathfrak k \mathfrak{k} -submodule of M are bounded by C
M
. In the present paper we describe explicitly all reductive in
\mathfrak s\mathfrak ln \mathfrak{s}{\mathfrak{l}_n} subalgebras
\mathfrak k \mathfrak{k} which admit a bounded simple infinite-dimensional (
\mathfrak s\mathfrak ln,\mathfrak k \mathfrak{s}{\mathfrak{l}_n},\mathfrak{k} )-module. Our technique is based on symplectic geometry and the notion of spherical variety. We also characterize the irreducible
components of the associated varieties of simple bounded (
\mathfrak g,\mathfrak k \mathfrak{g},\mathfrak{k} )-modules. 相似文献
12.
In a recent paper, F. Boca investigates the AF algebra
\mathfrak A{{\mathfrak{A}}} associated with the Farey-Stern-Brocot sequence. We show that
\mathfrak A{{\mathfrak{A}}} coincides with the AF algebra
\mathfrak M1{{\mathfrak{M_{1}}}} introduced by the present author in 1988. As proved in that paper (Adv. Math., vol.68.1), the K
0-group of
\mathfrak A{\mathfrak{A}} is the lattice-ordered abelian group M1{\mathcal{M}_{1}} of piecewise linear functions on the unit interval, each piece having integer coefficients, with the constant 1 as the distinguished
order unit. Using the elementary properties of M1{\mathcal{M}_{1}} we can give short proofs of several results in Boca’s paper. We also prove many new results: among others,
\mathfrak A{{\mathfrak{A}}} is a *-subalgebra of Glimm universal algebra, tracial states of
\mathfrak A{{\mathfrak{A}}} are in one-one correspondence with Borel probability measures on the unit real interval, all primitive ideals of
\mathfrak A{{\mathfrak{A}}} are essential. We describe the automorphism group of
\mathfrak A{{\mathfrak{A}}} . For every primitive ideal I of
\mathfrak A{{{\mathfrak{A}}}} we compute K
0( I) and
K0(\mathfrak A/ I){{K_{0}(\mathfrak{A}/I)}}. 相似文献
13.
Let V be a 2 m-dimensional symplectic vector space over an algebraically closed field K. Let $ \mathfrak{B}_n^{(f)} Let V be a 2m-dimensional symplectic vector space over an algebraically closed field K. Let
\mathfrakBn(f) \mathfrak{B}_n^{(f)} be the two-sided ideal of the Brauer algebra
\mathfrakBn( - 2m ) {\mathfrak{B}_n}\left( { - 2m} \right) over K generated by e
1
e
3⋯
e
2f-1 where 0 ≤ f ≤ [n/2]. Let HTf ?n \mathcal{H}\mathcal{T}_f^{ \otimes n} be the subspace of partial-harmonic tensors of valence f in V
⊗n
. In this paper we prove that dimHTf ?n \mathcal{H}\mathcal{T}_f^{ \otimes n} and dim
\textEn\textdK\textSp(V)( V ?n \mathord | / |
\vphantom V ?n V ?n V ?n\mathfrakBn(f) ) {\text{En}}{{\text{d}}_{K{\text{Sp}}(V)}}\left( {{{{V^{ \otimes n}}} \mathord{\left/{\vphantom {{{V^{ \otimes n}}} {{V^{ \otimes n}}}}} \right.} {{V^{ \otimes n}}}}\mathfrak{B}_n^{(f)}} \right) are both independent of K, and the natural homomorphism from
\mathfrakBn( - 2m ) \mathord | / |
\vphantom ( - 2m ) \mathfrakBn(f) \mathfrakBn(f) {\mathfrak{B}_n}{{\left( { - 2m} \right)} \mathord{\left/{\vphantom {{\left( { - 2m} \right)} {\mathfrak{B}_n^{(f)}}}} \right.} {\mathfrak{B}_n^{(f)}}} to
\textEn\textdK\textSp(V)( V ?n \mathord | / |
\vphantom V ?n V ?n V ?n\mathfrakBn(f) ) {\text{En}}{{\text{d}}_{K{\text{Sp}}(V)}}\left( {{{{V^{ \otimes n}}} \mathord{\left/{\vphantom {{{V^{ \otimes n}}} {{V^{ \otimes n}}}}} \right.} {{V^{ \otimes n}}}}\mathfrak{B}_n^{(f)}} \right) is always surjective. We show that HTf ?n \mathcal{H}\mathcal{T}_f^{ \otimes n} has a Weyl filtration and is isomorphic to the dual of
V ?n\mathfrakBn(f) \mathord | / |
\vphantom V ?n\mathfrakBn(f) V V ?n\mathfrakBn( f + 1 ) {{{{V^{ \otimes n}}\mathfrak{B}_n^{(f)}} \mathord{\left/{\vphantom {{{V^{ \otimes n}}\mathfrak{B}_n^{(f)}} V}} \right.} V}^{ \otimes n}}\mathfrak{B}_n^{\left( {f + 1} \right)} as an
\textSp(V) - ( \mathfrakBn( - 2m ) \mathord | / |
\vphantom ( - 2m ) \mathfrakBn( f + 1 ) \mathfrakBn( f + 1 ) ) {\text{Sp}}(V) - \left( {{\mathfrak{B}_n}{{\left( { - 2m} \right)} \mathord{\left/{\vphantom {{\left( { - 2m} \right)} {\mathfrak{B}_n^{\left( {f + 1} \right)}}}} \right.} {\mathfrak{B}_n^{\left( {f + 1} \right)}}}} \right) -bimodule. We obtain an
\textSp(V) - \mathfrakBn {\text{Sp}}(V) - {\mathfrak{B}_n} -bimodules filtration of V
⊗n
such that each successive quotient is isomorphic to some
?( l) ?zg,l\mathfrakBn \nabla \left( \lambda \right) \otimes {z_{g,\lambda }}{\mathfrak{B}_n} with λ ⊢ n 2g, ℓ(λ)≤m and 0 ≤ g ≤ [n/2], where ∇(λ) is the co-Weyl module associated to λ and z
g,λ is an explicitly constructed maximal vector of weight λ. As a byproduct, we show that each right
\mathfrakBn {\mathfrak{B}_n} -module
zg,l\mathfrakBn {z_{g,\lambda }}{\mathfrak{B}_n} is integrally defined and stable under base change. 相似文献
14.
Denote by γ the Gauss measure on ℝ
n
and by ${\mathcal{L}}${\mathcal{L}} the Ornstein–Uhlenbeck operator. In this paper we introduce a Hardy space
\mathfrak h1g{{\mathfrak{h}}^1}{{\rm \gamma}} of Goldberg type and show that for each u in ℝ ∖ {0} and r > 0 the operator ( rI+ L) iu(r{\mathcal{I}}+{\mathcal{L}})^{iu} is unbounded from
\mathfrak h1g{{\mathfrak{h}}^1}{{\rm \gamma}} to L
1γ. This result is in sharp contrast both with the fact that ( rI+ L) iu(r{\mathcal{I}}+{\mathcal{L}})^{iu} is bounded from H
1γ to L
1γ, where H
1γ denotes the Hardy type space introduced in Mauceri and Meda (J Funct Anal 252:278–313, 2007), and with the fact that in the Euclidean case ( rI-D) iu(r{\mathcal{I}}-\Delta)^{iu} is bounded from the Goldberg space
\mathfrak h1\mathbb Rn{{\mathfrak{h}}^1}{{\mathbb{R}}^n} to L
1ℝ
n
. We consider also the case of Riemannian manifolds M with Riemannian measure μ. We prove that, under certain geometric assumptions on M, an operator T{\mathcal{T}}, bounded on L
2
μ, and with a kernel satisfying certain analytic assumptions, is bounded from H
1
μ to L
1
μ if and only if it is bounded from
\mathfrak h1m{{\mathfrak{h}}^1}{\mu} to L
1
μ. Here H
1
μ denotes the Hardy space introduced in Carbonaro et al. (Ann Sc Norm Super Pisa, 2009), and
\mathfrak h1m{{\mathfrak{h}}^1}{\mu} is defined in Section 4, and is equivalent to a space recently introduced by M. Taylor (J Geom Anal 19(1):137–190, 2009). The case of translation invariant operators on homogeneous trees is also considered. 相似文献
15.
It is shown that indefinite strictly almost K?hler and opposite K?hler structures ( J, J′) on a four-dimensional manifold with J-invariant Ricci operator are rigid, thus extending a previous result of Apostolov, Armstrong and Drăghici from the positive
definite case to the indefinite one. In contrast to this, examples of nonhomogeneous four-dimensional manifolds which admit
strictly almost paraK?hler and opposite paraK?hler structures
(\mathfrak J,\mathfrak J¢){(\mathfrak{J},\mathfrak{J}^{\prime})} with
\mathfrak J{\mathfrak{J}} -invariant Ricci operator are shown. 相似文献
16.
We prove a function field analogue of the Herbrand-Ribet theorem on cyclotomic number fields. The Herbrand-Ribet theorem can
be interpreted as a result about cohomology with μ
p
-coefficients over the splitting field of μ
p
, and in our analogue both occurrences of μ
p
are replaced with the
\mathfrak p\mathfrak{p}-torsion scheme of the Carlitz module for a prime
\mathfrak p\mathfrak{p} in F
q
[ t]. 相似文献
17.
By using the concept of weight graph associated to nonsplit complex nilpotent Lie algebras \mathfrak g\mathfrak{g}, we find necessary and sufficient conditions for a semidirect product \mathfrak g? ? Ti\mathfrak{g}\overrightarrow{\oplus } T_{i} to be two-step solvable, where $T_{i} TT over \mathfrakg\mathfrak{g} which induces a decomposition of \mathfrakg\mathfrak{g} into one-dimensional weight spaces without zero weights. In particular we show that the semidirect product of such a Lie algebra with a maximal torus of derivations cannot be itself two-step solvable. We also obtain some applications to rigid Lie algebras, as a geometrical proof of the nonexistence of two-step nonsplit solvable rigid Lie algebras in dimensions n\geqslant 3n\geqslant 3. 相似文献
18.
The model 4-dimensional CR-cubic in ℂ 3 has the following “model” property: it is (essentially) the unique locally homogeneous 4-dimensional CR-manifold in ℂ 3 with finite-dimensional infinitesimal automorphism algebra
\mathfrak g\mathfrak{g} and non-trivial isotropy subalgebra. We study and classify, up to local biholomorphic equivalence, all
\mathfrak g\mathfrak{g}-homogeneous hypersurfaces in ℂ 3 and also classify the corresponding local transitive actions of the model algebra
\mathfrak g\mathfrak{g} on hypersurfaces in ℂ 3. 相似文献
19.
We consider a relationship between two sets of extensions of a finite finitely additive measure μ defined on an algebra
\mathfrakB \mathfrak{B} of sets to a broader algebra
\mathfrakA \mathfrak{A} . These sets are the set ex S
μ
of all extreme extensions of the measure μ and the set H
μ
of all extensions defined as
l(A) = [^(m)]( h(A) ), A ? \mathfrakA \lambda (A) = \hat{\mu }\left( {h(A)} \right),\,\,\,A \in \mathfrak{A} , where [^(m)] \hat{\mu } is a quotient measure on the algebra
\mathfrakB | / |
m {{\mathfrak{B}} \left/ {\mu } \right.} of the classes of μ-equivalence and
h:\mathfrakA ? \mathfrakB | / |
m h:\mathfrak{A} \to {{\mathfrak{B}} \left/ {\mu } \right.} is a homomorphism extending the canonical homomorphism
\mathfrakB \mathfrak{B} to
\mathfrakB | / |
m {{\mathfrak{B}} \left/ {\mu } \right.} . We study the properties of extensions from H
μ
and present necessary and sufficient conditions for the existence of these extensions, as well as the conditions under which
the sets ex S
μ
and H
μ
coincide. 相似文献
20.
The cohomology H
\mathfrakg\mathfrak{g}
) of the tangent Lie algebra
\mathfrakg\mathfrak{g}
of the group G with coefficients in the one-dimensional representation
\mathfrakg\mathfrak{g}
\mathbbK\mathbb{K}
defined by
[(W)\tilde] \mathfrakg \tilde \Omega _\mathfrak{g}
of H
1(G/
\mathfrakg\mathfrak{g}
. 相似文献
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