Symplectic representations of semidirect products

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Maria Sabitova
Keyword(s):  
Semidirect Products ◽  
Representations Of Groups ◽  
Symplectic Representations

Abstract.We study symplectic representations of groups of the form

Topological Left Amenability of Semidirect Products

1981 ◽  
Vol 24 (1) ◽  
pp. 79-85 ◽  
Author(s):  
H. D. Junghenn
Keyword(s):  
Large Class ◽  
Semidirect Product ◽  
Locally Compact ◽  
Semidirect Products ◽  
Topological Semigroups

AbstractLet S and T be locally compact topological semigroups and a semidirect product. Conditions are determined under which topological left amenability of S and T implies that of , and conversely. The results are used to show that for a large class of semigroups which are neither compact nor groups, various notions of topological left amenability coincide.

scholarly journals On finite degree partial representations of groups

2004 ◽  
Vol 274 (1) ◽  
pp. 309-334 ◽  
Author(s):  
M. Dokuchaev ◽  
N. Zhukavets
Keyword(s):  
Finite Degree ◽  
Representations Of Groups

Logic in representations of groups

2012 ◽  
Vol 51 (1) ◽  
pp. 1-27
Author(s):  
E. V. Aladova ◽  
A. Gvaramiya ◽  
B. Plotkin
Keyword(s):  
Representations Of Groups

scholarly journals VARIETIES OF REPRESENTATIONS OF GROUPS AND VARIETIES OF ASSOCIATIVE ALGEBRAS

2011 ◽  
Vol 21 (07) ◽  
pp. 1149-1178 ◽  
Author(s):  
ELENA ALADOVA ◽  
BORIS PLOTKIN
Keyword(s):  
General Theory ◽  
Group Representations ◽  
Associative Algebras ◽  
Open Problems ◽  
Representations Of Groups ◽  
Main Emphasis

This paper is tightly connected with the book [Varieties of Group Representations. General Theory, Connections and Applications (Zinatne, Riga, 1983) (in Russian)]. In the paper we prove new results in the spirit of the above-mentioned book. They are related to dimension subgroups, varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of associative algebras. We provide the reader with the list of open problems. For many reasons we consciously included in the text a brief review of the basic definitions and results from the theory of varieties of representations described in the book [Varieties of Group Representations. General Theory, Connections and Applications].

Unitary representations of groups, continuity and spectrum

2011 ◽  
Vol 97 (2) ◽  
pp. 157-165 ◽  
Author(s):  
Jean-Martin Paoli ◽  
Jean-Christophe Tomasi
Keyword(s):  
Unitary Representations ◽  
Representations Of Groups

scholarly journals Holomorphic Cohomology of Complex Analytic Linear Groups

1966 ◽  
Vol 27 (2) ◽  
pp. 531-542 ◽  
Author(s):  
G. Hochschild ◽  
G. D. Mostow
Keyword(s):  
Linear Group ◽  
Structure Theory ◽  
Linear Groups ◽  
Dimensional Representation ◽  
Lie Algebra Cohomology ◽  
Analytic Group ◽  
Finite Dimensional Representation ◽  
Semidirect Products ◽  
Finite Dimensional ◽  
Rational Cohomology

Let G be a complex analytic group, and let A be the representation space of a finite-dimensional complex analytic representation of G. We consider the cohomology for G in A, such as would be obtained in the usual way from the complex of holomorphic cochains for G in A. Actually, we shall use a more conceptual categorical definition, which is equivalent to the explicit one by cochains. In the context of finite-dimensional representation theory, nothing substantial is lost by assuming that G is a linear group. Under this assumption, it is the main purpose of this paper to relate the holomorphic cohomology of G to Lie algebra cohomology, and to the rational cohomology, in the sense of [1], of algebraic hulls of G. This is accomplished by using the known structure theory for complex analytic linear groups in combination with certain easily established results concerning the cohomology of semidirect products. The main results are Theorem 4.1 (whose hypothesis is always satisfied by a complex analytic linear group) and Theorems 5.1 and 5.2. These last two theorems show that the usual abundantly used connections between complex analytic representations of complex analytic groups and rational representations of algebraic groups extend fully to the superstructure of cohomology.

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