On Graded Simple Algebras

Details On Graded Simple Algebras On Graded Simple Algebras

2010-03-23

arxiv.org/abs/1003.4538v4

Mathematics

K-Theory and Homology

Updated version, with some corrections

Scientific paper

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.

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