EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 6 June 2010. For the current production of this journal, please refer to http://www.springer.com/mathematics/geometry/journal/40062.

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