Central simple superalgebras with anti-automorphisms of order two of the first kind

JOURNAL OF ALGEBRA

卷:323

Article

Jaber, Ameer

关键词: Anti-automorphisms;    Superalgebras;    Central simple superalgebras;    Superinvolutions;    Brauer groups;    Brauer-Wall groups;   

DOI  :  10.1016/j.jalgebra.2010.01.008

来源: Elsevier

【 摘 要 】

By a theorem of Albert's, a central simple associative algebra has an involution of the first kind if and only if it is of order 2 in the Brauer group. Our main purpose is to develop the theory of existence of anti-automorphisms of order 2 of the first kind on finite dimensional central simple associative superalgebras over K, where K is a field of arbitrary characteristic. First we need to generalize the Skolem-Noether Theorem to the superalgebra case. Then we show which kind of finite dimensional central simple superalgebras have an anti-automorphism of order 2 of the first kind. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free