Triangular Products of Group Representations and Their Applications by S M Vovsi
---------------------------------------------------------------
Author: S M Vovsi
Page Count: 142 pages
Published Date: 25 Feb 2012
Publisher: BIRKHAUSER BOSTON INC
Publication Country: Secaucus, United States
Language: English
ISBN: 9781468467239
File Name: Triangular.Products.of.Group.Representations.and.Their.Applications.pdf
Download Link: Triangular Products of Group Representations and Their Applications
---------------------------------------------------------------
Author: S M Vovsi
Page Count: 142 pages
Published Date: 25 Feb 2012
Publisher: BIRKHAUSER BOSTON INC
Publication Country: Secaucus, United States
Language: English
ISBN: 9781468467239
File Name: Triangular.Products.of.Group.Representations.and.Their.Applications.pdf
Download Link: Triangular Products of Group Representations and Their Applications
---------------------------------------------------------------
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 .
Read online Triangular Products of Group Representations and Their Applications Buy and read online Triangular Products of Group Representations and Their Applications Download and read Triangular Products of Group Representations and Their Applications for pc, mac, kindle, readers Download to iPad/iPhone/iOS, B&N nook Triangular Products of Group Representations and Their Applications ebook, pdf, djvu, epub, mobi, fb2, zip, rar, torrent
More posts:
Download PDF, EPUB, MOBI Twenty-Fourth Report of the Railroad Commission of Georgiathree lions pub shorewood menupages
Managing Your Career in the Music Industry download
Download Intelligent Computer Graphics 2009
Emily the Strange Stamps of Disapproval Kit pdf
Download ebook Sticky Assessment : Classroom Strategies to Amplify Student Learning