The Book of Involutions, Volume 44

Couverture
Max-Albert Knus
American Mathematical Soc., 30 juin 1998 - 593 pages
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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Table des matières

Involutions and Hermitian Forms l
1
Invariants of Involutions
71
Similitudes
153
Algebras of Degree Four
205
Algebras of Degree Three
279
Algebraic Groups
323
Galois Cohomology
383
Composition and Triality
451
Cubic Jordan Algebras
513
Trialitarian Central Simple Algebras
547
Bibliography
573
Index
585

Expressions et termes fréquents

Fréquemment cités

Page i - Interpolation and approximation by rational functions in the complex domain, 1935 19 REAC Paley and N. Wiener, Fourier transforms in the complex domain, 1934 18 M. Morse, The calculus of variations in the large, 1934 17 JM Wedderburn, Lectures on matrices, 1934 16 GA Bliss, Algebraic functions, 1933 15 MH Stone, Linear transformations in Hubert space and their applications to analysis...
Page 1 - Let V be a finite dimensional vector space over a field F.
Page xxi - Two sequences s and s' are called "equivalent" if they can be transformed into each other by a sequence of SHIFT-operations and s is called "canonical" if no more SHIFToperation is applicable.

Informations bibliographiques