共查询到20条相似文献,搜索用时 31 毫秒
1.
Boris Širola 《Central European Journal of Mathematics》2011,9(6):1317-1332
Let
\mathbbK\mathbb{K} be a field, G a reductive algebraic
\mathbbK\mathbb{K}-group, and G
1 ≤ G a reductive subgroup. For G
1 ≤ G, the corresponding groups of
\mathbbK\mathbb{K}-points, we study the normalizer N = N
G
(G
1). In particular, for a standard embedding of the odd orthogonal group G
1 = SO(m,
\mathbbK\mathbb{K}) in G = SL(m,
\mathbbK\mathbb{K}) we have N ≅ G
1 ⋊ μ
m
(
\mathbbK\mathbb{K}), the semidirect product of G
1 by the group of m-th roots of unity in
\mathbbK\mathbb{K}. The normalizers of the even orthogonal and symplectic subgroup of SL(2n,
\mathbbK\mathbb{K}) were computed in [Širola B., Normalizers and self-normalizing subgroups, Glas. Mat. Ser. III (in press)], leaving the proof
in the odd orthogonal case to be completed here. Also, for G = GL(m,
\mathbbK\mathbb{K}) and G
1 = O(m,
\mathbbK\mathbb{K}) we have N ≅ G
1 ⋊
\mathbbK\mathbb{K}
×. In both of these cases, N is a self-normalizing subgroup of G. 相似文献
2.
Let μ be a Poisson random measure, let
\mathbbF\mathbb{F} be the smallest filtration satisfying the usual conditions and containing the one generated by μ, and let
\mathbbG\mathbb{G} be the initial enlargement of
\mathbbF\mathbb{F} with the σ-field generated by a random variable G. In this paper, we first show that the mutual information between the enlarging random variable G and the σ-algebra generated by the Poisson random measure μ is equal to the expected relative entropy of the
\mathbbG\mathbb{G}-compensator relative to the
\mathbbF\mathbb{F}-compensator of the random measure μ. We then use this link to gain some insight into the changes of Doob–Meyer decompositions of stochastic processes when the
filtration is enlarged from
\mathbbF\mathbb{F} to
\mathbbG\mathbb{G}. In particular, we show that if the mutual information between G and the σ-algebra generated by the Poisson random measure μ is finite, then every square-integrable
\mathbbF\mathbb{F}-martingale is a
\mathbbG\mathbb{G}-semimartingale that belongs to the normed space S1\mathcal{S}^{1} relative to
\mathbbG\mathbb{G}. 相似文献
3.
Let
\mathbbF\mathbb{F} be a field of characteristic 0, and let G be an additive subgroup of
\mathbbF\mathbb{F}. We define a class of infinite-dimensional Lie algebras
\mathbbF\mathbb{F}-basis {L
μ, V
μ, W
μ | μ ∈ G}, which are very closely related to W-algebras. In this paper, the second cohomology group of is determined. 相似文献
4.
Swarnendu Datta 《Transformation Groups》2010,15(1):72-91
Let G be a commutative, unipotent, perfect, connected group scheme over an algebraically closed field of characteristic p > 0 and let E be a biextension of G × G by the discrete group
\mathbbQp/\mathbbZp\mathbb{Q}_{p}/\mathbb{Z}_{p}. When E is skew-symmetric, V. Drinfeld defined a certain metric group A associated to E (when G is the perfectization of the additive group
\mathbbGa\mathbb{G}_{a}, it is easy to compute this metric group, cf. Appendix A). In this paper we prove a conjecture due to Drinfeld about the
class of the metric group A in the Witt group (cf. Appendix B). 相似文献
5.
We determine which singular del Pezzo surfaces are equivariant compactifications of
\mathbbG\texta2 \mathbb{G}_{\text{a}}^2 , to assist with proofs of Manin’s conjecture for such surfaces. Additionally, we give an example of a singular quartic del
Pezzo surface that is an equivariant compactification of
\mathbbG\texta {\mathbb{G}_{\text{a}}} ⋊
\mathbbG\textm {\mathbb{G}_{\text{m}}} . Bibliography: 32 titles. 相似文献
6.
O. Yu. Dashkova 《Ukrainian Mathematical Journal》2012,63(9):1379-1389
We study a
\mathbbZG \mathbb{Z}G -module A such that
\mathbbZ \mathbb{Z} is the ring of integer numbers, the group G has an infinite sectional p-rank (or an infinite 0-rank), C
G
(A) = 1, A is not a minimax
\mathbbZ \mathbb{Z} -module, and, for any proper subgroup H of infinite sectional p-rank (or infinite 0-rank, respectively), the quotient module A/C
A
(H) is a minimax
\mathbbZ \mathbb{Z} -module. It is shown that if the group G is locally soluble, then it is soluble. Some properties of soluble groups of this kind are discussed. 相似文献
7.
Atsumu Sasaki 《Geometriae Dedicata》2010,145(1):151-158
Let G/K be an irreducible Hermitian symmetric space of non-compact type, and
G\mathbbC/K\mathbbC{G_{\mathbb{C}}/K_{\mathbb{C}}} its complexification by forgetting the original complex structure. Then,
D :=G\mathbbC/[K\mathbbC, K\mathbbC]{D :=G_{\mathbb{C}}/[K_{\mathbb{C}}, K_{\mathbb{C}}]} is a non-symmetric Stein manifold. We prove that a maximal compact subgroup of
G\mathbbC{G_{\mathbb{C}}} acts on D in a strongly visible fashion in the sense of Kobayashi (Publ Res Inst Math Sci 41:497–549, 2005) if and only if G/K is of non-tube type. Our proof uses the theory of multiplicity-free representations and a construction of a slice and an
anti-holomorphic involution on D. 相似文献
8.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
9.
Shikun OU 《Frontiers of Mathematics in China》2012,7(3):497-512
Let F be a field, and let
\mathbbG\mathbb{G} be the standard Borel subgroup of the symplectic group Sp(2m, F). In this paper, we characterize the bijective maps ϕ:
\mathbbG\mathbb{G} →
\mathbbG\mathbb{G} satisfying ϕ[x, y] = [ϕ(x), ϕ(y)]. 相似文献
10.
John R. Akeroyd 《Arkiv f?r Matematik》2011,49(1):1-16
It is shown that for any t, 0<t<∞, there is a Jordan arc Γ with endpoints 0 and 1 such that
G\{1} í \mathbbD:={z:|z| < 1}\Gamma\setminus\{1\}\subseteq\mathbb{D}:=\{z:|z|<1\}
and with the property that the analytic polynomials are dense in the Bergman space
\mathbbAt(\mathbbD\G)\mathbb{A}^{t}(\mathbb{D}\setminus\Gamma)
. It is also shown that one can go further in the Hardy space setting and find such a Γ that is in fact the graph of a continuous
real-valued function on [0,1], where the polynomials are dense in
Ht(\mathbbD\G)H^{t}(\mathbb{D}\setminus\Gamma)
; improving upon a result in an earlier paper. 相似文献
11.
Let G be a finite non-Abelian group. We define a graph Γ
G
; called the noncommuting graph of G; with a vertex set G − Z(G) such that two vertices x and y are adjacent if and only if xy ≠ yx: Abdollahi, Akbari, and Maimani put forward the following conjecture (the AAM conjecture): If S is a finite non-Abelian simple group and G is a group such that Γ
S
≅ Γ
G
; then S ≅ G: It is still unknown if this conjecture holds for all simple finite groups with connected prime graph except
\mathbbA10 {\mathbb{A}_{10}} , L
4(8), L
4(4), and U
4(4). In this paper, we prove that if
\mathbbA16 {\mathbb{A}_{16}} denotes the alternating group of degree 16; then, for any finite group G; the graph isomorphism
G\mathbbA16 @ GG {\Gamma_{{\mathbb{A}_{16}}}} \cong {\Gamma_G} implies that
\mathbbA16 @ G {\mathbb{A}_{16}} \cong G . 相似文献
12.
Christopher Hammond 《Mathematische Zeitschrift》2010,266(2):285-288
Let Ω be a domain in ${\mathbb{C}^{2}}Let Ω be a domain in
\mathbbC2{\mathbb{C}^{2}}, and let
p: [(W)\tilde]? \mathbbC2{\pi: \tilde{\Omega}\rightarrow \mathbb{C}^{2}} be its envelope of holomorphy. Also let W¢=p([(W)\tilde]){\Omega'=\pi(\tilde{\Omega})} with
i: W\hookrightarrow W¢{i: \Omega \hookrightarrow \Omega'} the inclusion. We prove the following: if the induced map on fundamental groups i*:p1(W) ? p1(W¢){i_{*}:\pi_{1}(\Omega) \rightarrow \pi_{1}(\Omega')} is a surjection, and if π is a covering map, then Ω has a schlicht envelope of holomorphy. We then relate this to earlier
work of Fornaess and Zame. 相似文献
13.
We study finite set-theoretic solutions (X,r) of the Yang-Baxter equation of square-free multipermutation type. We show that each such solution over ℂ with multipermutation
level two can be put in diagonal form with the associated Yang-Baxter algebra
A(\mathbbC,X,r)\mathcal{A}(\mathbb{C},X,r) having a q-commutation form of relations determined by complex phase factors. These complex factors are roots of unity and all roots
of a prescribed form appear as determined by the representation theory of the finite abelian group G\mathcal{G} of left actions on X. We study the structure of
A(\mathbbC,X,r)\mathcal{A}(\mathbb{C},X,r) and show that they have a ∙-product form ‘quantizing’ the commutative algebra of polynomials in |X| variables. We obtain the ∙-product both as a Drinfeld cotwist for a certain canonical 2-cocycle and as a braided-opposite
product for a certain crossed G\mathcal{G}-module (over any field k). We provide first steps in the noncommutative differential geometry of A(k,X,r)\mathcal{A}(k,X,r) arising from these results. As a byproduct of our work we find that every such level 2 solution (X,r) factorises as r = f ∘ τ ∘ f
− 1 where τ is the flip map and (X,f) is another solution coming from X as a crossed G\mathcal{G}-set. 相似文献
14.
Mahmoud Baroun Lahcen Maniar Roland Schnaubelt 《Integral Equations and Operator Theory》2009,65(2):169-193
We show the existence and uniqueness of the (asymptotically) almost periodic solution to parabolic evolution equations with
inhomogeneous boundary values on
\mathbbR{\mathbb{R}} and
\mathbbR±\mathbb{R}_{\pm}, if the data are (asymptotically) almost periodic. We assume that the underlying homogeneous problem satisfies the ‘Acquistapace–Terreni’
conditions and has an exponential dichotomy. If there is an exponential dichotomy only on half intervals ( − ∞, − T] and [T, ∞), then we obtain a Fredholm alternative of the equation on
\mathbbR{\mathbb{R}} in the space of functions being asymptotically almost periodic on
\mathbbR+{\mathbb{R}}_{+} and
\mathbbR-\mathbb{R}_{-}. 相似文献
15.
Affine extractors over prime fields 总被引:1,自引:0,他引:1
Amir Yehudayoff 《Combinatorica》2011,31(2):245-256
An affine extractor is a map that is balanced on every affine subspace of large enough dimension. We construct an explicit
affine extractor AE from
\mathbbFn \mathbb{F}^n to
\mathbbF\mathbb{F},
\mathbbF\mathbb{F} a prime field, so that AE(x) is exponentially close to uniform when x is chosen uniformly at random from an arbitrary affine subspace of
\mathbbFn \mathbb{F}^n of dimension at least δn, 0<δ≤1 a constant. Previously, Bourgain constructed such affine extractors when the size of
\mathbbF\mathbb{F} is two. Our construction is in the spirit of but different than Bourgain’s construction. This allows for simpler analysis
and better quantitative results. 相似文献
16.
Indranil Biswas 《Archiv der Mathematik》2005,84(1):38-45
Let EG be an algebraic principal G-bundle over
\mathbbC\mathbbPn ,\mathbb{C}\mathbb{P}^n , n
\mathbbC.\mathbb{C}. We prove that EG admits a reduction of structure group to a one-parameter subgroup of G if and only if
$
H^1 (\mathbb{C}\mathbb{P}^n ,{\text{ ad(}}E_G )( - k)) = 0
$
H^1 (\mathbb{C}\mathbb{P}^n ,{\text{ ad(}}E_G )( - k)) = 0
相似文献
17.
A variety ${\mathbb{V}}${\mathbb{V}} is var-relatively universal if it contains a subvariety
\mathbbW{\mathbb{W}} such that the class of all homomorphisms that do not factorize through any algebra in
\mathbbW{\mathbb{W}} is algebraically universal. And
\mathbbV{\mathbb{V}} has an algebraically universal α-expansion
a\mathbbV{\alpha\mathbb{V}} if adding α nullary operations to all algebras in
\mathbbV{\mathbb{V}} gives rise to a class
a\mathbbV{\alpha\mathbb{V}} of algebras that is algebraically universal. The first two authors have conjectured that any varrelative universal variety
\mathbbV{\mathbb{V}} has an algebraically universal α-expansion
a\mathbbV{\alpha\mathbb{V}} . This note contains a more general result that proves this conjecture. 相似文献
18.
Alexander Premet 《Inventiones Mathematicae》2010,181(2):395-420
Let ${\mathfrak{g}}
19.
We define a rank variety for a module of a noncocommutative Hopf algebra
A = L \rtimes GA = \Lambda \rtimes G where
L = k[X1, ..., Xm]/(X1l, ..., Xml), G = (\mathbbZ/l\mathbbZ)m\Lambda = k[X_1, \dots, X_m]/(X_1^{\ell}, \dots, X_m^{\ell}), G = (\mathbb{Z}/\ell\mathbb{Z})^m and char k does not divide ℓ, in terms of certain subalgebras of A playing the role of “cyclic shifted subgroups”. We show that the rank variety of a finitely generated module M is homeomorphic to the support variety of M defined in terms of the action of the cohomology algebra of A. As an application we derive a theory of rank varieties for the algebra Λ. When ℓ=2, rank varieties for Λ-modules were constructed
by Erdmann and Holloway using the representation theory of the Clifford algebra. We show that the rank varieties we obtain
for Λ-modules coincide with those of Erdmann and Holloway. 相似文献
20.
GURMEET K BAKSHI SHALINI GUPTA INDER BIR S PASSI 《Proceedings Mathematical Sciences》2011,121(4):379-396
Given a group G of order p
1
p
2, where p
1, p
2 are primes, and
\mathbbFq\mathbb{F}_{q}, a finite field of order q coprime to p
1
p
2, the object of this paper is to compute a complete set of primitive central idempotents of the semisimple group algebra
\mathbbFq[G]\mathbb{F}_{q}[G]. As a consequence, we obtain the structure of
\mathbbFq[G]\mathbb{F}_{q}[G] and its group of automorphisms. 相似文献
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