Homomorphisms from AH-algebras
Huaxin Lin

TL;DR
This paper characterizes when two unital monomorphisms from an AH-algebra to a simple C*-algebra with low tracial rank are approximately unitarily equivalent, based on K-theoretic and tracial data, extending to continuous functions on compact spaces.
Contribution
It provides a complete classification of monomorphisms from AH-algebras to certain simple C*-algebras using K-theory and trace invariants, including an approximate version.
Findings
Characterization of approximate unitary equivalence via K-theory and trace maps.
Extension of classification to continuous functions on compact metric spaces.
Existence theorem for monomorphisms with prescribed invariants.
Abstract
Let be a general unital AH-algebra and let be a unital simple -algebra with tracial rank at most one. Suppose that are two unital monomorphisms. We show that and are approximately unitarily equivalent if and only if \beq[\phi]&=&[\psi] {\rm in} KL(C,A), \phi_{\sharp}&=&\psi_{\sharp}\tand \phi^{\dag}&=&\psi^{\dag}, \eneq where and are continuous affine maps from tracial state space of to faithful tracial state space of induced by and respectively, and and are induced homomorphisms from into where is the space of all real affine continuous functions on and is the closure of the image of in the affine space In particular, the…
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Algebraic structures and combinatorial models
