Relative K-theory for C^*-algebras

2021/06/04 by Haslehurst, Mitch
#46L80 #46M20 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2106.02620

Abstract

Given C^*-algebras A and B and a ^*-homomorphism ϕ:A→ B, we adopt the portrait of the relative K-theory K_*(ϕ) due to Karoubi using Banach categories and Banach functors. We show that the elements of the relative groups may be represented in a simple form. We prove the existence of two six-term exact sequences, and we use these sequences to deduce the fact that the relative theory is isomorphic, in a natural way, to the K-theory of the mapping cone.

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