Triangular Products of Group Representations and Their Applications - Progress in Mathematics - S. M. Vovsi - Books - Birkhauser Boston Inc - 9781468467239 - February 25, 2012
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Triangular Products of Group Representations and Their Applications - Progress in Mathematics Softcover Reprint of the Original 1st Ed. 1981 edition

S. M. Vovsi

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Triangular Products of Group Representations and Their Applications - Progress in Mathematics Softcover Reprint of the Original 1st Ed. 1981 edition

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 .


132 pages, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released February 25, 2012
Original release date 1981
ISBN13 9781468467239
Publishers Birkhauser Boston Inc
Pages 132
Dimensions 155 × 235 × 7 mm   ·   213 g
Language English