Finite-dimensional division algebras over fields
By: Nathan Jacobson.
Publisher: Springer
Published: 1996
Place of publication: Berlin; New York
Language: eng
Number of pages: 278
Subjects: Division algebras; Algebraic fields
Description: Finite-dimensional division algebras over fields determine, by the Wedderburn 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. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts; they arose first in the study of the so-called "multiplication algebras of Riemann matrices".

The largest part of the book is the fifth chapter, dealing with involutorial simple algebras of finite dimension over a field. Of particular interest are the Jordan algebras determined by these algebras with involution; their structure is discussed. Two important concepts of these algebras with involution are the universal enveloping algebras and the reduced norm.
Notes: Includes bibliographical references (p. 275-278)