共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we give the eigenvalues of the manifold Sp(n)/U(n). We prove that an eigenvalue λ
s
(f
2, f
2, …, f
n
) of the Lie group Sp(n), corresponding to the representation with label (f
1, f
2, ..., f
n
), is an eigenvalue of the manifold Sp(n)/U(n), if and only if f
1, f
2, …, f
n
are all even. 相似文献
2.
Lingli Wang 《Frontiers of Mathematics in China》2010,5(1):179-190
Let G be a finite group, and let π
e
(G) be the spectrum of G, that is, the set of all element orders of G. In 1987, Shi Wujie put forward the following conjecture. If G is a finite group and M is a non-abelian simple group, then G ≅ M if and only if |G| = |M| and π
e
(G) = π
e
(M). In this short paper, we prove that if G is a finite group, then G ≅ M if and only if |G| = |M| and π
e
(G) = π
e
(M), where M = D
n
(2) and n is even. 相似文献
3.
Yu. V. Volkov 《Vestnik St. Petersburg University: Mathematics》2008,41(1):9-14
A classification up to stable equivalence of representation-finite self-injective algebras with associated Dynkin diagram D n is suggested. In each stable equivalence class, a representative is chosen, and the representatives are partitioned into five families of algebras, which are described in terms of quivers with relations. 相似文献
4.
Let O
n
be the order-preserving transformation semigroup on X
n
. For an arbitrary integer r such that 1≤r≤n−2, we completely describe the maximal regular subsemibands of the semigroup K(n,r)={α∈O
n
:|im(α)|≤r}. We also formulate the cardinal number of such subsemigroups. 相似文献
5.
The purpose of this paper is to investigate central elements in distribution algebras D i s t(G) of general linear supergroups G = G L(m|n). As an application, we compute explicitly the center of D i s t(G L(1|1)) and its image under Harish-Chandra homomorphism. 相似文献
6.
We characterise (residually-finite) groups which possess less than n subgroups of index n for almost all n ∈ ℕ. 相似文献
7.
Antônio BrandãoJr. 《Rendiconti del Circolo Matematico di Palermo》2008,57(2):265-278
Let M
n
(K) be the algebra of all n × n matrices over an infinite field K. This algebra has a natural ℤ
n
-grading and a natural ℤ-grading. Finite bases for its ℤ
n
-graded identities and for its ℤ-graded identities are known. In this paper we describe finite generating sets for the ℤ
n
-graded and for the ℤ-graded central polynomials for M
n
(K)
Partially supported by CNPq 620025/2006-9 相似文献
8.
Behrooz Mirzaii 《Mathematische Annalen》2008,340(1):159-184
The homology of GL
n
(R) and SL
n
(R) is studied, where R is a commutative ‘ring with many units’. Our main theorem states that the natural map H
4(GL3(R), k) → H
4(GL4(R), k) is injective, where k is a field with char(k) ≠ 2, 3. For an algebraically closed field F, we prove a better result, namely, is injective. We will prove a similar result replacing GL by SL. This is used to investigate the indecomposable part of the
K-group K
4(R). 相似文献
9.
We show that if a finite simple group G, isomorphic to PSLn(q) or PSUn(q) where either n ≠ 4 or q is prime or even, acts on a vector space over a field of the defining characteristic of G; then the corresponding semidirect product contains an element whose order is distinct from every element order of G. We infer that the group PSLn(q), n ≠ 4 or q prime or even, is recognizable by spectrum from its covers thus giving a partial positive answer to Problem 14.60 from the Kourovka Notebook. 相似文献
10.
The natural automorphism group of a translation surface is its group of translations. For finite translation surfaces of genus g ≥ 2 the order of this group is naturally bounded in terms of g due to a Riemann–Hurwitz formula argument. In analogy with classical Hurwitz surfaces, we call surfaces which achieve the maximal bound Hurwitz translation surfaces. We study for which g there exist Hurwitz translation surfaces of genus g. 相似文献
11.
Florian Herzig 《Inventiones Mathematicae》2011,186(2):373-434
Let F be a finite extension of ℚ
p
. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} to be supersingular. We then give the classification of irreducible admissible smooth GL
n
(F)-representations over
[`( \mathbbF)]p\overline{ \mathbb{F}}_{p} in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel–Livné for n=2. For general split reductive groups we obtain similar results under stronger hypotheses. 相似文献
12.
V. I. Zenkov 《Siberian Mathematical Journal》2016,57(6):1002-1010
Given a finite group G with socle isomorphic to L 2(q), q ≥ 4, we describe, up to conjugacy, all pairs of nilpotent subgroups A and B of G such that A ∩ B g ≠ 1 for all g ∈ G. 相似文献
13.
Given an indexing set I and a finite field Kα for each α ∈ I, let ? = {L2(Kα) | α ∈ I} and \(\mathfrak{N} = \{ SL_2 (K_\alpha )|\alpha \in I\}\). We prove that each periodic group G saturated with groups in \(\Re (\mathfrak{N})\) is isomorphic to L2(P) (respectively SL2(P)) for a suitable locally finite field P. 相似文献
14.
P. A. Valinevih 《Journal of Mathematical Sciences》2010,168(6):811-819
We propose a method for construction of the general solution of the Yang–Baxter equation with the U
q
(sℓ
n
) symmetry algebra. This method is based on the factorization property of the corresponding L-operator. We present a closed-form expression for the universal R-matrix in the form of a difference operator acting on the
space of functions of n(n − 1) variables. Bibliography: 16 titles. 相似文献
15.
A subgroup K of G is Mp-supplemented in G if there exists a subgroup B of G such that G = KB and TB < G for every maximal subgroup T of K with |K: T| = pα. In this paper we prove the following: Let p be a prime divisor of |G| and let H be ap-nilpotent subgroup having a Sylow p-subgroup of G. Suppose that H has a subgroup D with Dp ≠ 1 and |H: D| = pα. Then G is p-nilpotent if and only if every subgroup T of H with |T| = |D| is Mp-supplemented in G and NG(Tp)/CG(Tp) is a p-group. 相似文献
16.
Dong-il Lee 《Algebras and Representation Theory》2010,13(6):705-718
In this note, we find a monomial basis of the cyclotomic Hecke algebra \({\mathcal{H}_{r,p,n}}\) of G(r,p,n) and show that the Ariki-Koike algebra \({\mathcal{H}_{r,n}}\) is a free module over \({\mathcal{H}_{r,p,n}}\), using the Gröbner-Shirshov basis theory. For each irreducible representation of \({\mathcal{H}_{r,p,n}}\), we give a polynomial basis consisting of linear combinations of the monomials corresponding to cozy tableaux of a given shape. 相似文献
17.
Paola De Vito 《Ricerche di matematica》2011,60(1):39-43
We prove that if q = p
h
, p a prime, do not exist sets U í AG(n,q){U {\subseteq} AG(n,q)}, with |U| = q
k
and 1 < k < n, determining N directions where
\fracqk - 1p - 1 < N £ \fracq+32 q k-1+ qk-2 +...+q2 + q \frac{{q^k} - 1}{p - 1} < N \le \frac{q+3}{2} q ^{k-1}+ q^{k-2} +\dots+q{^2} + q 相似文献
18.
In this paper we consider n-poised planar node sets, as well as more special ones, called G C n sets. For the latter sets each n-fundamental polynomial is a product of n linear factors as it always holds in the univariate case. A line ? is called k-node line for a node set \(\mathcal X\) if it passes through exactly k nodes. An (n + 1)-node line is called maximal line. In 1982 M. Gasca and J. I. Maeztu conjectured that every G C n set possesses necessarily a maximal line. Till now the conjecture is confirmed to be true for n ≤ 5. It is well-known that any maximal line M of \(\mathcal X\) is used by each node in \(\mathcal X\setminus M, \)meaning that it is a factor of the fundamental polynomial. In this paper we prove, in particular, that if the Gasca-Maeztu conjecture is true then any n-node line of G C n set \(\mathcal {X}\) is used either by exactly \(\binom {n}{2}\) nodes or by exactly \(\binom {n-1}{2}\) nodes. We prove also similar statements concerning n-node or (n ? 1)-node lines in more general n-poised sets. This is a new phenomenon in n-poised and G C n sets. At the end we present a conjecture concerning any k-node line. 相似文献
19.
Let k be a field and E(n) be the 2
n+1-dimensional pointed Hopf algebra over k constructed by Beattie, Dăscălescu and Grünenfelder [J. Algebra, 2000, 225: 743–770]. E(n) is a triangular Hopf algebra with a family of triangular structures R
M
parameterized by symmetric matrices M in M
n
(k). In this paper, we study the Azumaya algebras in the braided monoidal category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
and obtain the structure theorems for Azumaya algebras in the category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
, where M is any symmetric n×n matrix over k. 相似文献
20.
T. Na 《Siberian Mathematical Journal》2017,58(4):718-726
Suppose that F is a formation of finite groups. We introduce the concept of F h -supplemented subgroups and investigate the structure of finite groups on assuming that some maximal subgroups of Sylow subgroups, maximal subgroups, minimal subgroups, and 2-maximal subgroup are F h -supplemented, respectively. Some available results are generalized. 相似文献
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