On the non-neutral component of outer forms of the orthogonal group

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

First, Uriya A.¹ 

[1] Univ Haifa, Haifa, Israel

关键词: Central simple algebra;    Brauer group;    Involution;    Orthogonal group;    Azumaya algebra;    Reduced norm;   

DOI  :  10.1016/j.jpaa.2020.106477

来源: Elsevier

【 摘 要 】

Let (A, sigma) be a central simple algebra with an orthogonal involution. It is well-known that O(A, sigma) contains elements of reduced norm -1 if and only if the Brauer class of A is trivial. We generalize this statement to Azumaya algebras with orthogonal involution over semilocal rings, and show that the if part fails if one allows the base ring to be arbitrary. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free