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On Graded Simple Algebras
#
On Graded Simple Algebras

##
Roozbeh Hazrat and Judith R. Millar

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.

Journal of Homotopy and Related Structures, Vol. 5(2010), No. 1, pp. 113-124