On graded simple algebras

zbMATH Open1278.19006arXiv1003.4538MaRDI QIDQ390698

Judith R. Millar, Roozbeh Hazrat

Publication date: 8 January 2014

Published in: Journal of Homotopy and Related Structures (Search for Journal in Brave)

Abstract: 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, ,igeq 0, are the Quillen K-groups.

Full work available at URL: https://arxiv.org/abs/1003.4538

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

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