Finite-Dimensional Division Algebras Over Fields

Download or read book Finite-Dimensional Division Algebras Over Fields written by Nathan Jacobson and published by Springer Science & Business Media. This book was released on 1996 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite-dimensional division algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensio= nal algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brau= er-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 involu= torial 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. Corrections of the 1st edition (1996) carried out on behalf of N. Jacobson (deceased) by Prof. P.M. Cohn (UC London, UK).