the book of involutions
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The Book of Involutions
by Alexander Merkurjev (Author), Markus Rost (Author), Jean-Pierre Tignol (Author), Max-Albert Knus
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Book 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
Product Details
Hardcover: 593 pages
Publisher: American Mathematical Society
(October 1998)
Language: English
ISBN-10: 0821809040
ISBN-13: 978-0821809044
Product Dimensions: 10.3 x 7.2 x 1.5 inches
Shipping Weight: 2.8 pounds
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