Completely Reducible Infinite-Dimensional Skew Linear Groups

2000 ◽  
Vol 129 (2) ◽  
pp. 153-157 ◽  
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Linear Groups ◽  
Infinite Dimensional ◽  
Completely Reducible

ON SOME INFINITE DIMENSIONAL LINEAR GROUPS

2001 ◽  
Vol 29 (2) ◽  
pp. 519-527
Author(s):  
L. A. Kurdachenko ◽  
I. Ya. Subbotin
Keyword(s):  
Linear Groups ◽  
Infinite Dimensional

Simple Cn modules with multiplicities 1 and applications

1994 ◽  
Vol 72 (7-8) ◽  
pp. 326-335 ◽  
Author(s):  
D. J. Britten ◽  
J. Hooper ◽  
F. W. Lemire
Keyword(s):  
Weyl Group ◽  
Tensor Products ◽  
Weight Space ◽  
One Dimensional ◽  
Infinite Dimensional ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Recursion Formulas ◽  
Completely Reducible ◽  
Index 2

In this paper we show that there exist exactly two nonequivalent simple infinite dimensional highest weight Cn modules having the property that every weight space is one dimensional. The tensor products of these modules with any finite-dimensional simple Cn module are proven to be completely reducible and we provide an explicit decomposition for such tensor products. As an application of these decompositions, we obtain two recursion formulas for computing the multiplicities of simple finite dimensional Cn modules. These formulas involve a sum over subgroups of index 2 in the Weyl group of Cn.

scholarly journals Generalisations of nilpotency of rings

1973 ◽  
Vol 18 (4) ◽  
pp. 265-272 ◽  
Author(s):  
Edmund F. Robertson
Keyword(s):  
Linear Groups ◽  
Infinite Dimensional

In (5) and (6) we studied certain subgroups of infinite dimensional linear groups over rings. In particular we investigated how the structure of the subgroups was related to the structure of the rings over which the linear groups were defined. It became clear that it might prove useful to study generalised nilpotent properties of rings analogous to Baer nilgroups and Gruenberg groups. We look briefly at some classes of generalised nilpotent rings in this paper and obtain a lattice diagram exhibiting all the strict inclusions between the classes.

On an analogue of a theorem of P. Hall for infinite dimensional linear groups

2019 ◽  
Vol 6 (2) ◽  
pp. 577-589
Author(s):  
Martyn R. Dixon ◽  
Leonid A. Kurdachenko ◽  
Igor Ya. Subbotin
Keyword(s):  
Linear Groups ◽  
Infinite Dimensional

Infinite dimensional linear groups

1978 ◽  
Vol 78 (3-4) ◽  
pp. 237-240 ◽  
Author(s):  
D. G. Arrell ◽  
E. F. Robertson
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Normal Structure ◽  
General Linear ◽  
Noetherian Rings ◽  
Linear Groups ◽  
Infinite Dimensional

SynopsisIn this paper we show that some of Bass' results on the normal structure of the stable general linear group can be extended to infinite dimensional linear groups over non-commutative Noetherian rings.

scholarly journals On the structure of some infinite dimensional linear groups

2016 ◽  
Vol 45 (1) ◽  
pp. 234-246 ◽  
Author(s):  
Martyn R. Dixon ◽  
Leonid A. Kurdachenko ◽  
Javier Otal
Keyword(s):  
Linear Groups ◽  
Infinite Dimensional

On some infinite dimensional linear groups

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Leonid Kurdachenko ◽  
Alexey Sadovnichenko ◽  
Igor Subbotin
Keyword(s):  
Vector Space ◽  
Present Article ◽  
Linear Groups ◽  
Infinite Dimensional

AbstractLet F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.

scholarly journals Finitarily linear wreath products

2000 ◽  
Vol 43 (1) ◽  
pp. 27-41
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Finite Dimension ◽  
Wreath Products ◽  
Vector Spaces ◽  
Normal Subgroups ◽  
Infinite Dimensional ◽  
Linear Representations ◽  
Finitary Linear ◽  
Completely Reducible ◽  
Necessary And Sufficient ◽  
Standard Wreath Product

AbstractWe consider faithful finitary linear representations of (generalized) wreath products A wrΩH of groups A by H over (potentially) infinite-dimensional vector spaces, having previously considered completely reducible such representations in an earlier paper. The simpler the structure of A the more complex, it seems, these representations can become. If A has no non-trivial abelian normal subgroups, the conditions we present are both necessary and sufficient. They imply, for example, that for such an A, if there exists such a representation of the standard wreath product A wr H of infinite dimension, then there already exists one of finite dimension.

On some infinite dimensional linear groups

2003 ◽  
pp. 377-384 ◽  
Author(s):  
Leonid Kurdachenko ◽  
Igor Subbotin
Keyword(s):  
Linear Groups ◽  
Infinite Dimensional
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