ENGLISH

The book of involutions

By Alexander Merkurjev , Markus Rost , and Jean-Pierre Tignol Max-Albert Knus , Max-Albert Knus

Book information

Publisher
American Mathematical Society
Year
1998
ISBN
9780821809044, 0821809040
LCC
QA179 .B66 1998
Open Library ID
OL362027M
Language
english
Format
PDF
Filesize
3 MB (3589750 bytes)
Series
Amer Mathematical Soc
Pages
588\588
Topic
Mathematics Algebra
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields. Involutions are viewed as twisted forms of (hermitian) quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are also discussed, as well as groups of type $F_4$ or $G_2$ arising from exceptional Jordan or composition algebras. Several results and notions appear here for the first time, notably the discriminant algebra of an algebra with unitary involution and the algebra-theoretic counterpart to linear groups of type $D_4$. This volume also contains a Bibliography and Index. Features: original material not in print elsewhere a comprehensive discussion of algebra-theoretic and group-theoretic aspects extensive notes that give historical perspective and a survey on the literature rational methods that allow possible generalization to more general base rings.

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