Ebook: The book of involutions
Author: Knus Max-Albert et al.
- Genre: Mathematics // Algebra
- Tags: Linear algebraic groups., Hermitian forms., Homology theory., Galois theory.
- Series: Colloquium publications (American Mathematical Society) 44
- Year: 1998
- Publisher: American Mathematical Society
- City: Providence, R.I
- Language: English
- djvu
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