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Triangular Products of Group Representations and Their Applications

  • Book
  • © 1981

Overview

Authors:
  1. Samuel M. Vovsi

    1. Riga Polytechnic Institute, Riga, USSR

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Part of the book series: Progress in Mathematics (PM, volume 17)

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Table of contents (2 chapters)

  1. Front Matter

    Pages i-ix
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  2. Triangular Products

    • Samuel M. Vovsi
    Pages 1-56

  3. Applications

    • Samuel M. Vovsi
    Pages 57-114

  4. Back Matter

    Pages 115-131
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Keywords

About this book

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 .

Authors and Affiliations

  • Riga Polytechnic Institute, Riga, USSR

    Samuel M. Vovsi

Bibliographic Information

  • Book Title: Triangular Products of Group Representations and Their Applications

  • Authors: Samuel M. Vovsi

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4684-6721-5

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 1981

  • Softcover ISBN: 978-1-4684-6723-9Published: 25 February 2012

  • eBook ISBN: 978-1-4684-6721-5Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: X, 132

  • Topics: Group Theory and Generalizations

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