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arXiv · 2307.15639

Remarks on computing the Grothendieck rings of C*-algebras

E. Ghamari·C. Ingalls·D. Kucerovsky
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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 $\mathbb{C}$, $\mathbb{R}$, and $\mathbb{H}$.

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E. Ghamari, C. Ingalls, D. Kucerovsky. 2023-07-28. Remarks on computing the Grothendieck rings of C*-algebras. https://arxiv.org/abs/2307.15639

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