On Graded Simple Algebras

2010/03/23 by Roozbeh Hazrat, Hazrat, R., Judith R Millar +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1003.4538

openalex publication_date 2010/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, i≥ 0, are the Quillen K-groups.

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