{"product_id":"triangular-products-of-group-representations-and-their-applications-softcover-reprint-of-the-original-1st-1981","title":"Triangular Products of Group Representations and Their Applications (Softcover Reprint of the Original 1st 1981)","description":"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 .","brand":"Birkhauser","offers":[{"title":"Default Title","offer_id":51160177017143,"sku":"9781468467239","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0934\/9926\/1239\/files\/imageloader_6817e41a-b877-4794-a1ab-9441d00ac8c6.jpg?v=1759425496","url":"https:\/\/shop.queerbooks.com\/products\/triangular-products-of-group-representations-and-their-applications-softcover-reprint-of-the-original-1st-1981","provider":"Philly AIDS Thrift @ Giovanni's Room","version":"1.0","type":"link"}