Triangular Products of Group Representations and Their Applications: 17 (Progress in Mathematics) - Softcover

Vovsi, S.M.

 
9781468467239: Triangular Products of Group Representations and Their Applications: 17 (Progress in Mathematics)
Softcover
ISBN 10: 1468467239 ISBN 13: 9781468467239
Verlag: Birkhäuser, 2012

Inhaltsangabe

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 .

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Reseña del editor

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 .

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Birkhäuser
Erscheinungsdatum
2012
Sprache
Englisch
ISBN 10 
1468467239
ISBN 13 
9781468467239
Einband
Tapa blanda
Anzahl der Seiten
144
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar

Weitere beliebte Ausgaben desselben Titels

9783764330620: Triangular Products of Group Representations and Their Applications: v. 17 (Progress in Mathematics)

Vorgestellte Ausgabe

ISBN 10:  3764330627 ISBN 13:  9783764330620
Verlag: Birkhauser Verlag AG, 1982
Hardcover