Articles liés à Finite-Dimensional Division Algebras over Fields

Finite-Dimensional Division Algebras over Fields - Couverture rigide

Jacobson, Nathan

 
9783540570295: Finite-Dimensional Division Algebras over Fields
Couverture rigide
ISBN 10 : 3540570292 ISBN 13 : 9783540570295
Editeur : Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1996

Synopsis

These algebras determine, by the Sliedderburn Theorem. the semi-simple finite dimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brauer-Severi varieties. Sie shall be interested in these algebras which have an involution. Algebras with involution arose first in the study of the so-called .'multiplication algebras of Riemann matrices". Albert undertook their study at the behest of Lefschetz. He solved the problem of determining these algebras. The problem has an algebraic part and an arithmetic part which can be solved only by determining the finite dimensional simple algebras over an algebraic number field. We are not going to consider the arithmetic part but will be interested only in the algebraic part. In Albert's classical book (1939). both parts are treated. A quick survey of our Table of Contents will indicate the scope of the present volume. The largest part of our book is the fifth chapter which deals with invo- torial rimple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution. Their structure is determined and two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm. Of great importance is the concept of isotopy. There are numerous applications of these concepts, some of which are quite old.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Date d'édition
1996
Langue
anglais
ISBN 10 
3540570292
ISBN 13 
9783540570295
Reliure
Relié
Numéro d'édition
1
Nombre de pages
292
Coordonnées du fabricant
non disponible
Personne responsable
CMN Printpool Inh. Mathis Neumann
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