ISBN: 9781468467239 - triangular products of group representations and their applications (progress in mathematics, band 17) (14 Ergebnisse)

Zustand: New.

Zustand: New. In English.

Zustand: New. 2012. Softcover reprint of the original 1st ed. 1981. paperback. . . . . .

Zustand: New. pp. 144.

Zustand: New. 2012. Softcover reprint of the original 1st ed. 1981. paperback. . . . . . Books ship from the US and Ireland.

Zustand: New.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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 .…

Zustand: As New. Unread book in perfect condition.

Zustand: new. Questo è un articolo print on demand.

PF. Zustand: New. This item is printed on demand. Brand new book, sourced directly from publisher. Dispatch time is 6-7 days from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely.

Taschenbuch. Zustand: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 . 144 pp. Englisch.…

Zustand: New. Print on Demand pp. 144 49:B&W 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam.

Zustand: New. PRINT ON DEMAND pp. 144.

Taschenbuch. Zustand: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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 .Springer Nature c/o IBS, Benzstrasse 21, 48619 Heek 144 pp. Englisch. …