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Finite-Dimensional Division Algebras Over Fields

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Finite-Dimensional Division Algebras Over Fields Cover

 

Synopses & Reviews

Publisher Comments:

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).

Synopsis:

Here, the eminent algebraist, Nathan Jacobsen, concentrates on those algebras that have an involution. Although they appear in many contexts, these algebras first arose in the study of the so-called "multiplication algebras of Riemann matrices". Of particular interest are the Jordan algebras determined by such algebras, and thus their structure is discussed in detail. Two important concepts also dealt with are the universal enveloping algebras and the reduced norm. However, the largest part of the book is the fifth chapter, which focuses on involutorial simple algebras of finite dimension over a field.

Product Details

ISBN:
9783540570295
Author:
Jacobson, Nathan
Publisher:
Springer
Location:
Berlin ;
Subject:
Group Theory
Subject:
Algebraic fields
Subject:
Division algebras.
Subject:
Algebra - General
Subject:
Geometry - Algebraic
Subject:
Mathematics-Group Theory
Subject:
Associative rings.
Subject:
Commutative rings
Subject:
Nonassociative
Subject:
ring theory
Subject:
Algebra
Edition Description:
Enlarged 1994.
Series Volume:
22
Publication Date:
20111031
Binding:
HARDCOVER
Language:
English
Illustrations:
Yes
Pages:
286
Dimensions:
235 x 155 mm 1290 gr

Related Subjects

Health and Self-Help » Health and Medicine » Medical Specialties
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Geometry » Algebraic Geometry
Science and Mathematics » Mathematics » Group Theory

Finite-Dimensional Division Algebras Over Fields New Hardcover
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Product details 286 pages Springer - English 9783540570295 Reviews:
"Synopsis" by , Here, the eminent algebraist, Nathan Jacobsen, concentrates on those algebras that have an involution. Although they appear in many contexts, these algebras first arose in the study of the so-called "multiplication algebras of Riemann matrices". Of particular interest are the Jordan algebras determined by such algebras, and thus their structure is discussed in detail. Two important concepts also dealt with are the universal enveloping algebras and the reduced norm. However, the largest part of the book is the fifth chapter, which focuses on involutorial simple algebras of finite dimension over a field.
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