Finite-dimensional division algebras over fields
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Word Count
69,500 words, Guess
Page Count
278 pages
Identifiers
- Open LibraryOL993122M
- ISBN-103540570292
- OCLC Control Number35095954
- OCLC Control Numberfinitedimensiona00jaco
- Library of Congress Control Numbertmp96031625
and 1 more
- Goodreads4945421
Classifications
- DDC512/.24
- LCCQA247.45 .J33 1996
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.
Subjects
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