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1.
《代数通讯》2013,41(7):3519-3527
Abstract Let G and A be finite groups such that (|G|, |A|) = 1. Let K be an algebraically closed field with Char K = 0. Denote by K α G the twisted group algebra of G over K with factor set α. In this paper we prove that if A acts homogeneously on K α G, then there exists an action of A on G, and there is a one-to-one correspondence between the set of A-invariant irreducible K α G-modules and the set of irreducible K α C G (A)-modules. 相似文献
2.
Let φ be a Drinfeld A-module of arbitrary rank and arbitrary characteristic over a finitely generated field K, and set GK=Gal(Ksep/K). Let E=EndK(φ). We show that for almost all primes p of A the image of the group ring A[GK] in EndA(Tp(φ)) is the commutant of E. In the special case E=A it follows that the representation of GK on the p-torsion points φ[p](Ksep) of φ is absolutely irreducible for almost all p. 相似文献
3.
We compute the Drinfel’d double for the bicrossproduct multiplier Hopf algebra A = k[G] ⋊ K(H) associated with the factorization of an infinite group M into two subgroups G and H. We also show that there is a basis-preserving self-duality structure for the multiplier Hopf algebra A = k[G] ⋊ K(H) if there is a factor-reversing group isomorphism.
Presented by A. Verschoren. 相似文献
4.
Xiang-dong Hou 《Graphs and Combinatorics》1992,8(1):53-64
LetG be a finite abelian group,K a subfield ofC, C[G] regarded as an algebra of matrices.A
G
K
{AC[G]| all the entries and eigenvalues ofA are inK} is an association algebra overK. In this paper, the association scheme ofA
G
K
is determined and in the caseK=Q(i), the first eigenmatrix of the association scheme computed. As an application, it is proved thatZ
4×Z
4×Z
4 is the only abelian group admitted as a Singer group by some distance-regular digraph of girth 4 on 64 vertices. 相似文献
5.
Fátima Araújo 《Geometriae Dedicata》2011,154(1):133-160
We consider a homogeneous fibration G/L → G/K, with symmetric fiber and base, where G is a compact connected semisimple Lie group and L has maximal rank in G. We suppose the base space G/K is isotropy irreducible and the fiber K/L is simply connected. We investigate the existence of G-invariant Einstein metrics on G/L such that the natural projection onto G/K is a Riemannian submersion with totally geodesic fibers. These spaces are divided in two types: the fiber K/L is isotropy irreducible or is the product of two irreducible symmetric spaces. We classify all the G-invariant Einstein metrics with totally geodesic fibers for the first type. For the second type, we classify all these metrics
when G is an exceptional Lie group. If G is a classical Lie group we classify all such metrics which are the orthogonal sum of the normal metrics on the fiber and
on the base or such that the restriction to the fiber is also Einstein. 相似文献
6.
We study the K-theory of unital C*-algebras A satisfying the condition that all irreducible representations are finite and of some bounded dimension. We construct
computational tools, but show that K-theory is far from being able to distinguish between various interesting examples. For example, when the algebra A is n-homogeneous, i.e., all irreducible representations are exactly of dimension n, then K*(A) is the topological K-theory of a related compact Hausdorff space, this generalises the classical Gelfand-Naimark theorem, but there are many inequivalent
homogeneous algebras with the same related topological space. For general A we give a spectral sequence computing K*(A) from a sequence of topological K-theories of related spaces. For A generated by two idempotents, this becomes a 6-term long exact sequence. 相似文献
7.
Let G be a finite group and let p be a prime such that (p, |G|) = 1. We study conditions under which the Abelian group
p
[G] has a few G-orbits whose union generate it as an expander (equivalently, all the discrete Fourier coefficients (in absolute value) of this generating set are bounded away uniformly from one).We prove a (nearly sharp) bound on the distribution of dimensions of irreducible representations of G which implies the existence of such expanding orbits. We further show a class of groups for which such a bound follows from the expansion properties of G. Together, these lead to a new iterative construction of expanding Cayley graphs of nearly constant degree. 相似文献
8.
LetK[G] denote the group algebra of the finite groupG over the non-absolute fieldK of characteristic ≠ 2, and let *:K[G] →K[G] be theK-involution determined byg*=g
−1 for allg ∈G. In this paper, we study the group A = A(K[G]) of unitary units ofK[G] and we classify those groupsG for which A contains no nonabelian free group. IfK is algebraically closed, then this problem can be effectively studied via the representation theory ofK[G]. However, for general fields, it is preferable to take an approach which avoids having to consider the division rings involved.
Thus, we use a result of Tits to construct fairly concrete free generators in numerous crucial special cases.
The first author’s research was supported in part by Capes and Fapesp - Brazil.
The second author’s research was supported in part by NSF Grant DMS-9224662. 相似文献
9.
Let K be a finitely generated field of transcendence degree 1 over a finite field, and set GK?Gal(Ksep/K). Let φ be a Drinfeld A-module over K in special characteristic. Set E?EndK(φ) and let Z be its center. We show that for almost all primes p of A, the image of the group ring Ap[GK] in EndA(Tp(φ)) is the commutant of E. Thus, for almost all p it is a full matrix ring over Z⊗AAp. In the special case E=A it follows that the representation of GK on the p-torsion points φ[p] is absolutely irreducible for almost all p. 相似文献
10.
I. Lizasoain 《数学学报(英文版)》2010,26(3):405-418
Some classical results about linear representations of a finite group G have been also proved for representations of G on non-abelian groups (G-groups). In this paper we establish a decomposition theorem for irreducible G-groups which expresses a suitable irreducible G-group as a tensor product of two projective G-groups in a similar way to the celebrated theorem of Clifford for linear representations. Moreover, we study the non-abelian minimal normal subgroups of G in which this decomposition is possible. 相似文献
11.
Let G be a non-compact connected semisimple Lie group with finite center and let GK denote the centralizer of a maximal compact subgroup K of G inG, the universal enveloping algebra over of the Lie algebra of G. In [4] Lepowsky defines an injective anti-homo morphism P:G
KK
MA, where M is the centralizer in K of a Cartan subalgebraa of the symmetric pair (G,K),K andA are the universal enveloping algebras over corresponding to K anda, respectively, andK
M is the centralizer of M inK. The subalgebra P(G
K) ofK
MA has considerable significance in the infinite dimensional representation theory of G. In this paper we explicitly compute P(G
K) when G=S0o(4,1), and show how this result leads to the determination of all irreducible representations of G and its universal covering group Spin(4,1).Partially supported by CONICET (Argentina) grants. 相似文献
12.
Let H and K be normal subgroups of a finite group G and let K≤H. If A is a subgroup of G such that AH=AK or A∩H=A∩K, we say that A covers or avoids H/K respectively. The purpose of this paper is to investigate factor groups of a finite group G using this concept. We get some characterizations of a finite group being solvable or supersolvable and generalize some known results. 相似文献
13.
Mark L. Lewis 《代数通讯》2013,41(4):1273-1292
A finite group G is odd-square-free if no irreducible complex character of G has degree divisible by the square of an odd prime. We determine all odd-square-free groups G satisfying S ≤ G ≤ Aut(S) for a finite simple group S. More generally, we show that if G is any nonsolvable odd-square-free group, then G has at most two nonabelian chief factors and these must be simple odd-square-free groups. If the alternating group A 7 is involved in G, the structure of G can be further restricted. 相似文献
14.
Dimitrios Poulakis 《Monatshefte für Mathematik》2000,129(2):139-145
On the reduction modulo
p
of absolutely irreducible polynomials. Let K be a number field and F(X,Y) be an absolutely irreducible polynomial of K[X,Y]. In this note, using an effective version of Riemann-Roch theorem and a version of the implicit functions theorem, we calculate
a positive number A such that if ℘ is prime ideal of the ring of integers of K with norm , then the reduction of F(X,Y) modulo ℘ is an absolutely irreducible polynomial.
(Réu le 1 Février 1999; en forme finale 21 Septembre 1999) 相似文献
15.
The structure of the algebra K[M] of the plactic monoid M of rank 3 over a field K is studied. The minimal prime ideals of K[M] are described. There are only two such ideals and each of them is a principal ideal determined by a homogeneous congruence
on M. Moreover, in case K is uncountable and algebraically closed, the left and right primitive spectrum and the corresponding irreducible representations
of the algebra K[M] are described. All these representations are monomial. As an application, a new proof of the semiprimitivity of K[M] is given. 相似文献
16.
In the present paper we investigate the relationship between the complex representations of an association scheme G and the complex representations of certain factor schemes of G. Our first result is that, similar to group representation theory, representations of factor schemes over normal closed subsets
of G can be viewed as representations of G itself. We then give necessary and sufficient conditions for an irreducible character of G to be a character of a factor scheme of G. These characterizations involve the central primitive idempotents of the adjacency algebra of G and they are obtained with the help of the Frobenius reciprocity low which we prove for complex adjacency algebras.
Received: February 27, 2001 Final version received: August 30, 2001 相似文献
17.
IfK is an infinite field and ifG=GL(n, K) with the discrete topology, then all principal-series representations ofG are irreducible, and any two such with the same central character ψ are weakly equivalent to one another and to the ψ-regular
representation. In addition, every irreducible unitary representation ofG which is not one-dimensional weakly contains a representation of the principal series. We deduce that every maximal ideal
ofC*(G) is either of codimension 1 or else a kernel of a principal-series representation. In particular, except in the exceptional
case whereK is an infinite algebraic extension of a finite field, the reducedC*-algebra of PGL(n, K) is simple, as was also shown by de la Harpe in many cases.
Partially supported by NSF Grant DMS-85-06130. It is a pleasure also to acknowledge the hospitality of the Institute for Advanced
Studies, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel, from January to August, 1988.
Partially supported by NSF Grants DMS-84-00900 and DMS-87-00551. Much of this work was done while visiting at, and partially
supported by, the Department of Mathematics and Computer Science, Bar-Ilan University, 52100 Ramat Gan, Israel. 相似文献
18.
We develop a duality theory between the continuous representations of a compactp-adic Lie groupG in Banach spaces over a givenp-adic fieldK and certain compact modules over the completed group ringo
K[[G]]. We then introduce a “finiteness” condition for Banach space representations called admissibility. It will be shown that
under this duality admissibility corresponds to finite generation over the ringK[[G]]: =K ⊗o
K[[G]]. Since this latter ring is noetherian it follows that the admissible representations ofG form an abelian category. We conclude by analyzing the irreducibility properties of the continuous principal series of the
groupG: = GL2(ℤ
p
). 相似文献
19.
Hung P. Tong-Viet 《Algebras and Representation Theory》2012,15(2):379-389
Let G be a finite group. Denote by Irr(G) the set of all irreducible complex characters of G. Let cd(G) be the set of all irreducible complex character degrees of G forgetting multiplicities, that is, cd(G) = {χ(1) : χ ∈ Irr(G)} and let cd
*(G) be the set of all irreducible complex character degrees of G counting multiplicities. Let H be an alternating group of degree at least 5, a sporadic simple group or the Tits group. In this paper, we will show that
if G is a non-abelian simple group and cd(G) í cd(H)cd(G)\subseteq cd(H) then G must be isomorphic to H. As a consequence, we show that if G is a finite group with cd*(G) í cd*(H)cd^*(G)\subseteq cd^*(H) then G is isomorphic to H. This gives a positive answer to Question 11.8 (a) in (Unsolved problems in group theory: the Kourovka notebook, 16th edn) for alternating groups, sporadic simple groups or
the Tits group. 相似文献
20.
Shaun Stevens 《Inventiones Mathematicae》2008,172(2):289-352
Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic.
We construct many new supercuspidal representations of G, and Bushnell–Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation
of G arises from our constructions. 相似文献