{"product_id":"9781468467239","title":"Progress in Mathematics","description":"\u003ch1\u003eProgress in Mathematics\u003c\/h1\u003e \u003ch2\u003eVovsi, S.M.\u003c\/h2\u003e \u003cp\u003eThe 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 .\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2012-02-25\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9781468467239\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-1-4684-6721-5\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 132\u003c\/p\u003e ","brand":"Birkhäuser Boston","offers":[{"title":"Default Title","offer_id":44450527117452,"sku":"9781468467239","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781468467239.jpg?v=1775736525","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9781468467239","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}