关于正交群外形的非中性分支
On the non-neutral component of outer forms of the orthogonal group
摘要：
设$(A,σ)$是具有正交对合的中心单代数.众所周知，$O(A,σ)$包含约化范数$-1$的元素当且仅当$A$的Brauer类是平凡的。我们将这一陈述推广到半局部环上具有正交对合的Azumaya代数，并证明如果允许基环是任意的，则“如果”部分失败。
英文摘要：
Let $(A,σ)$ be a central simple algebra with an orthogonal involution. It is well-known that $O(A,σ)$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
