operator algebras

Obstructions to homomorphisms between homogeneous C*-algebras

arXiv:2607.13222

summary

The paper develops a method to detect new obstructions to the existence of homomorphisms between homogeneous C*-algebras with prescribed K‑theory behavior, and uses it to fully resolve a 1993 problem of Blackadar about unital homomorphisms between matrix‑valued function algebras on even spheres that are injective on K₀.

Abstract

We develop a method to find new obstructions to the existence of homomorphisms between homogeneous C*-algebras with prescribed behavior on K-theory. As an application, we give a complete answer to a problem posed by Blackadar in 1993 concerning the existence of unital homomorphisms between algebras of matrix-valued functions on even spheres which are injective on K_0: we show that if n, d, k, r are natural numbers and k is not in the range n, n+1, ..., n+d-1, then there is no unital homomorphism from C (S^{2n}, M_r) to C (S^{2k}, M_{dr}) which is injective on K_0.

33 pages

Topics & keywords

#homogeneous c*-algebras#k-theory#homomorphism obstructions#matrix-valued functions#even spheres#blackadar problemC*-algebraK₀unital homomorphismobstruction theorymatrix-valued functionssphere
Obstructions to homomorphisms between homogeneous C*-algebras · wovepaper