Remarks on computing the Grothendieck rings of C*-algebras

2023/07/28 by Ghamari, E., Ingalls, C., Kucerovsky, D.
#FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2307.15639

Abstract

In this paper, we present a captivating construction by Grothendieck, originally formulated for algebraic varieties, and adapt it to the realm of C*-algebras. Our main objective is to investigate the conditions under which this particular class of C*-algebras possesses a nontrivial Grothendieck ring. To achieve this, we explore the existence of nontrivial characters, which significantly enriches our understanding of these algebras. In particular, we conduct a detailed study of rings of C*-algebras over ℂ, ℝ, and ℍ.

Related

• Ring C*-algebras
• Grothendieck Categories
• Does the Grothendieck ring of varieties contain nilpotent elements?
• The log Grothendieck ring of varieties
• Symmetries of Grothendieck rings in representation theory