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The book of involutions

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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  Read more...

Abstract: 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

Author(s): Knus, Max-Albert et al.
Series: Colloquium publications (American Mathematical Society) 44
Publisher: American Mathematical Society
Year: 1998

Language: English
Pages: 617
City: Providence, R.I
Tags: Linear algebraic groups.;Hermitian forms.;Homology theory.;Galois theory.

Content: Involutions and Hermitian forms Invariants of involutions Similitudes Algebras of degree four Algebras of degree three Algebraic groups Galois cohomology Composition and triality Cubic Jordan algebras Trialitarian central simple algebras.