关于分次单代数
On Graded Simple Algebras
摘要：
本文首先指出，一个分次中心单代数，被一个阿贝尔群分次，是一个分次Azumaya代数，并且它在它的中心上是自由的.本文证明了分次Azumaya代数A在中心$R$上自由时，K_i^{ \gr }（A）与K_i^{ \gr }（R）“非常接近”，其中K_i^{ \gr }（R）定义为K_i（\Pgr（R））.这里\Pgr（R）是分次生成投射R-模范畴，K_i，i，i \geq 0，是Quillen K-群.
英文摘要：
This note begins by observing that a graded central simple algebra, graded by an abelian group, is a graded Azumaya algebra and it is free over its centre. For a graded Azumaya algebra A free over its centre $R$, we show that K_i^{\gr} (A) is "very close" to K_i^{\gr}(R), where K_i^{\gr} (R) is defined to be K_i(\Pgr (R)). Here \Pgr (R) is the category of graded finitely generated projective R-modules and K_i, \,i\geq 0, are the Quillen K-groups.
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。
