共查询到20条相似文献,搜索用时 109 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.
We prove that the symplectic group
Sp(2n,\mathbbZ){Sp(2n,\mathbb{Z})} and the mapping class group Mod
S
of a compact surface S satisfy the R
∞ property. We also show that B
n
(S), the full braid group on n-strings of a surface S, satisfies the R
∞ property in the cases where S is either the compact disk D, or the sphere S
2. This means that for any automorphism f{\phi} of G, where G is one of the above groups, the number of twisted f{\phi}-conjugacy classes is infinite. 相似文献
3.
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
4.
5.
F. V. Petrov 《Journal of Mathematical Sciences》2007,147(6):7218-7226
Let Γ ⊂ ℝd be a bounded strictly convex surface. We prove that the number kn(Γ) of points of Γ that lie on the lattice
satisfies the following estimates: lim inf kn(Γ)/nd−2 < ∞ for d ≥ 3 and lim inf kn(Γ)/log n < ∞ for d = 2. Bibliography: 9 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 344, 2007, pp. 174–189. 相似文献
6.
A. Arkhipova 《Journal of Mathematical Sciences》2011,176(6):732-758
We prove the existence of a global heat flow u : Ω ×
\mathbbR+ ? \mathbbRN {\mathbb{R}^{+}} \to {\mathbb{R}^{N}}, N > 1, satisfying a Signorini type boundary condition u(∂Ω ×
\mathbbR+ {\mathbb{R}^{+}}) ⊂
\mathbbRn {\mathbb{R}^{n}}),
n \geqslant 2 n \geqslant 2 , and
\mathbbRN {\mathbb{R}^{N}}) with boundary ∂
[`(W)] \bar{\Omega } such that φ(∂Ω) ⊂
\mathbbRN {\mathbb{R}^{N}} is given by a smooth noncompact hypersurface S. Bibliography: 30 titles. 相似文献
7.
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
8.
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
9.
Christopher Kennedy 《Algebras and Representation Theory》2011,14(6):1187-1202
This paper continues the study of associative and Lie deep matrix algebras,
DM(X,\mathbbK){\mathcal{DM}}(X,{\mathbb{K}}) and
\mathfrakgld(X,\mathbbK){\mathfrak{gld}}(X,{\mathbb{K}}), and their subalgebras. After a brief overview of the general construction, balanced deep matrix subalgebras,
BDM(X,\mathbbK){\mathcal{BDM}}(X,{\mathbb{K}}) and
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}), are defined and studied for an infinite set X. The global structures of these two algebras are studied, devising a depth grading on both as well as determining their ideal
lattices. In particular,
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}) is shown to be semisimple. The Lie algebra
\mathfrakbld(X,\mathbbK){\mathfrak{bld}}(X,{\mathbb{K}}) possesses a deep Cartan decomposition and is locally finite with every finite subalgebra naturally enveloped by a semi-direct
product of
\mathfraksln{\mathfrak{{sl}_n}}’s. We classify all associative bilinear forms on
\mathfraksl2\mathfrakd{\mathfrak{sl}_2\mathfrak{d}} (a natural depth analogue of
\mathfraksl2{\mathfrak{{sl}_2}}) and
\mathfrakbld{\mathfrak{bld}}. 相似文献
10.
V. M. Prokip 《Ukrainian Mathematical Journal》2012,63(8):1314-1320
Polynomial n × n matrices A(x) and B(x) over a field
\mathbbF \mathbb{F} are called semiscalar equivalent if there exist a nonsingular n × n matrix P over
\mathbbF \mathbb{F} and an invertible n × n matrix Q(x) over
\mathbbF \mathbb{F} [x] such that A(x) = PB(x)Q(x). We give a canonical form with respect to semiscalar equivalence for a matrix pencil A(x) = A
0x
- A
1, where A
0 and A
1 are n × n matrices over
\mathbbF \mathbb{F} , and A
0 is nonsingular. 相似文献
11.
Let (Ω , F , P ) be a probability space and L0 ( F, R ) the algebra of equivalence classes of real- valued random variables on (Ω , F , P ). When L0 ( F, R ) is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0 ( F, R ) to L0 ( F, R ). As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module ( S,|| · ||) is random uniformly convex iff Lp ( S ) is uniformly convex for each fixed positive number p such that 1 p + ∞ . 相似文献
12.
S. E. Pastukhova 《Journal of Mathematical Sciences》2012,181(5):668-700
We consider the operator exponential e
−tA
, t > 0, where A is a selfadjoint positive definite operator corresponding to the diffusion equation in
\mathbbRn {\mathbb{R}^n} with measurable 1-periodic coefficients, and approximate it in the operator norm
|| · ||L2( \mathbbRn ) ? L2( \mathbbRn ) {\left\| {\; \cdot \;} \right\|_{{{L^2}\left( {{\mathbb{R}^n}} \right) \to {L^2}\left( {{\mathbb{R}^n}} \right)}}} with order
O( t - \fracm2 ) O\left( {{t^{{ - \frac{m}{2}}}}} \right) as t → ∞, where m is an arbitrary natural number. To construct approximations we use the homogenized parabolic equation with constant
coefficients, the order of which depends on m and is greater than 2 if m > 2. We also use a collection of 1-periodic functions N
α
(x),
x ? \mathbbRn x \in {\mathbb{R}^n} , with multi-indices α of length
| a| \leqslant m \left| \alpha \right| \leqslant m , that are solutions to certain elliptic problems on the periodicity cell. These results are used to homogenize the diffusion
equation with ε-periodic coefficients, where ε is a small parameter. In particular, under minimal regularity conditions, we construct approximations of order O(ε
m
) in the L
2-norm as ε → 0. Bibliography: 14 titles. 相似文献
13.
P. Mironescu 《Journal of Mathematical Sciences》2010,170(3):340-355
We describe the structure of the space
Ws,p( \mathbbSn;\mathbbS1 ) {W^{s,p}}\left( {{\mathbb{S}^n};{\mathbb{S}^1}} \right) , where 0 < s < ∞ and 1 ≤ p < ∞. According to the values of s, p, and n, maps in
Ws,p( \mathbbSn;\mathbbS1 ) {W^{s,p}}\left( {{\mathbb{S}^n};{\mathbb{S}^1}} \right) can either be characterised by their phases or by a couple (singular set, phase). 相似文献
14.
Harold Widom proved in 1966 that the spectrum of a Toeplitz operator T(a) acting on the Hardy space
Hp(\mathbbT)H^p({\mathbb{T}}) over the unit circle
\mathbbT{\mathbb{T}} is a connected subset of the complex plane for every bounded measurable symbol a and 1 < p < ∞. In 1972, Ronald Douglas established the connectedness of the essential spectrum of T(a) on
H2(\mathbbT)H^2({\mathbb{T}}). We show that, as was suspected, these results remain valid in the setting of Hardy spaces Hp(Γ,w), 1 < p < ∞, with general Muckenhoupt weights w over arbitrary Carleson curves Γ. 相似文献
15.
Alexander Premet 《Inventiones Mathematicae》2010,181(2):395-420
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
16.
B. Enriquez 《Selecta Mathematica, New Series》2001,7(3):321-407
To any field
\Bbb K \Bbb K of characteristic zero, we associate a set
(\mathbbK) (\mathbb{K}) and a group
G0(\Bbb K) {\cal G}_0(\Bbb K) . Elements of
(\mathbbK) (\mathbb{K}) are equivalence classes of families of Lie polynomials subject to associativity relations. Elements of
G0(\Bbb K) {\cal G}_0(\Bbb K) are universal automorphisms of the adjoint representations of Lie bialgebras over
\Bbb K \Bbb K . We construct a bijection between
(\mathbbK)×G0(\Bbb K) (\mathbb{K})\times{\cal G}_0(\Bbb K) and the set of quantization functors of Lie bialgebras over
\Bbb K \Bbb K . This construction involves the following steps.? 1) To each element v \varpi of
(\mathbbK) (\mathbb{K}) , we associate a functor
\frak a?\operatornameShv(\frak a) \frak a\mapsto\operatorname{Sh}^\varpi(\frak a) from the category of Lie algebras to that of Hopf algebras;
\operatornameShv(\frak a) \operatorname{Sh}^\varpi(\frak a) contains
U\frak a U\frak a .? 2) When
\frak a \frak a and
\frak b \frak b are Lie algebras, and
r\frak a\frak b ? \frak a?\frak b r_{\frak a\frak b} \in\frak a\otimes\frak b , we construct an element
?v (r\frak a\frak b) {\cal R}^{\varpi} (r_{\frak a\frak b}) of
\operatornameShv(\frak a)?\operatornameShv(\frak b) \operatorname{Sh}^\varpi(\frak a)\otimes\operatorname{Sh}^\varpi(\frak b) satisfying quasitriangularity identities; in particular,
?v(r\frak a\frak b) {\cal R}^\varpi(r_{\frak a\frak b}) defines a Hopf algebra morphism from
\operatornameShv(\frak a)* \operatorname{Sh}^\varpi(\frak a)^* to
\operatornameShv(\frak b) \operatorname{Sh}^\varpi(\frak b) .? 3) When
\frak a = \frak b \frak a = \frak b and
r\frak a ? \frak a?\frak a r_\frak a\in\frak a\otimes\frak a is a solution of CYBE, we construct a series
rv(r\frak a) \rho^\varpi(r_\frak a) such that
?v(rv(r\frak a)) {\cal R}^\varpi(\rho^\varpi(r_\frak a)) is a solution of QYBE. The expression of
rv(r\frak a) \rho^\varpi(r_\frak a) in terms of
r\frak a r_\frak a involves Lie polynomials, and we show that this expression is unique at a universal level. This step relies on vanishing
statements for cohomologies arising from universal algebras for the solutions of CYBE.? 4) We define the quantization of a
Lie bialgebra
\frak g \frak g as the image of the morphism defined by ?v(rv(r)) {\cal R}^\varpi(\rho^\varpi(r)) , where
r ? \mathfrakg ?\mathfrakg* r \in \mathfrak{g} \otimes \mathfrak{g}^* .<\P> 相似文献
17.
We obtain a representation for the sharp coefficient in an estimate of the modulus of the nth derivative of an analytic function in the upper half-plane
\mathbbC+ {\mathbb{C}_{+} } . It is assumed that the boundary value of the real part of the function on
?\mathbbC+ \partial {\mathbb{C}_{+} } belongs to L
p
. This representation is specified for p = 1 and p = 2. For p = ∞ and for derivatives of odd order, an explicit formula for the sharp coefficient is found. A limit relation for the sharp
coefficient in a pointwise estimate for the modulus of the n-th derivative of an analytic function in a disk is found as the point approaches the boundary circle. It is assumed that
the boundary value of the real part of the function belongs to L
p
. The relation in question contains the sharp constant from the estimate of the modulus of the n-th derivative of an analytic function in
\mathbbC+ {\mathbb{C}_{+} } . As a corollary, a limit relation for the modulus of the n-th derivative of an analytic function with the bounded real part is obtained in a domain with smooth boundary. Bibliography:
8 titles. 相似文献
18.
A. Vourdas 《Journal of Fourier Analysis and Applications》2010,16(5):748-767
Harmonic analysis on ℤ(p
ℓ
) and the corresponding representation of the Heisenberg-Weyl group HW[ℤ(p
ℓ
),ℤ(p
ℓ
),ℤ(p
ℓ
)], is studied. It is shown that the HW[ℤ(p
ℓ
),ℤ(p
ℓ
),ℤ(p
ℓ
)] with a homomorphism between them, form an inverse system which has as inverse limit the profinite representation of the
Heisenberg-Weyl group
\mathfrak HW[\mathbbZp,\mathbbZp,\mathbbZp]\mathfrak {HW}[{\mathbb{Z}}_{p},{\mathbb{Z}}_{p},{\mathbb{Z}}_{p}]. Harmonic analysis on ℤ
p
is also studied. The corresponding representation of the Heisenberg-Weyl group HW[(ℚ
p
/ℤ
p
),ℤ
p
,(ℚ
p
/ℤ
p
)] is a totally disconnected and locally compact topological group. 相似文献
19.
This paper presents rules for numerical integration over spherical caps and discusses their properties. For a spherical cap
on the unit sphere
\mathbbS2\mathbb{S}^2, we discuss tensor product rules with n
2/2 + O(n) nodes in the cap, positive weights, which are exact for all spherical polynomials of degree ≤ n, and can be easily and inexpensively implemented. Numerical tests illustrate the performance of these rules. A similar derivation
establishes the existence of equal weight rules with degree of polynomial exactness n and O(n
3) nodes for numerical integration over spherical caps on
\mathbbS2\mathbb{S}^2. For arbitrary d ≥ 2, this strategy is extended to provide rules for numerical integration over spherical caps on
\mathbbSd\mathbb{S}^d that have O(n
d
) nodes in the cap, positive weights, and are exact for all spherical polynomials of degree ≤ n. We also show that positive weight rules for numerical integration over spherical caps on
\mathbbSd\mathbb{S}^d that are exact for all spherical polynomials of degree ≤ n have at least O(n
d
) nodes and possess a certain regularity property. 相似文献
20.
Two natural extensions of Jensen’s functional equation on the real line are the equations f(xy) + f(xy
−1) = 2f(x) and f(xy) + f(y
−1
x) = 2f(x), where f is a map from a multiplicative group G into an abelian additive group H. In a series of papers (see Ng in Aequationes Math 39:85–99, 1990; Ng in Aequationes Math 58:311–320, 1999; Ng in Aequationes Math 62:143–159, 2001), Ng solved these functional equations for the case where G is a free group and the linear group
GLn(R), R=\mathbbZ,\mathbbR{{GL_n(R), R=\mathbb{Z},\mathbb{R}}} , is a quadratically closed field or a finite field. He also mentioned, without a detailed proof, in the above papers and
in (see Ng in Aequationes Math 70:131–153, 2005) that when G is the symmetric group S
n
, the group of all solutions of these functional equations coincides with the group of all homomorphisms from (S
n
, ·) to (H, + ). The aim of this paper is to give an elementary and direct proof of this fact. 相似文献