Triangular Products of Group Representations and Their Applications (Paperback, Softcover reprint of the original 1st ed. 1981)

The construction considered in these notes is based on a very simple idea. Let (A, G ) and (B, G ) be two group representations, for definiteness faithful and finite 1 2 dimensional, over an arbitrary field. We shall say that a faithful representation (V, G) is an extension of (A, G ) by (B, G ) if there is a G-submodule W of V such that 1 2 the naturally arising representations (W, G) and (V/W, G) are isomorphic, modulo their kernels, to (A, G ) and (B, G ) respectively. 1 2 Question. Among all the extensions of (A, G ) by (B, G ), does there exist 1 2 such a "universal" extension which contains an isomorphic copy of any other one? The answer is in the affirmative. Really, let dim A = m and dim B = n, then the groups G and G may be considered as matrix groups of degrees m and n 1 2 respectively. If (V, G) is an extension of (A, G ) by (B, G ) then, under certain 1 2 choice of a basis in V, all elements of G are represented by (m + n) x (m + n) mat rices of the form (*) ~1-~ ~-J lh I g2 I .

General

Imprint:	Birkhauser Boston
Country of origin:	United States
Series:	Progress in Mathematics, 17
Release date:	February 2012
First published:	February 2012
Authors:	S. M Vovsi
Dimensions:	235 x 155 x 7mm (L x W x T)
Format:	Paperback
Pages:	132
Edition:	Softcover reprint of the original 1st ed. 1981
ISBN-13:	978-1-4684-6723-9
Categories:	Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory Promotions
LSN:	1-4684-6723-9
Barcode:	9781468467239

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