Work

On the homotopy groups of the automorphism groups of Cuntz–Krieger algebras

Year: 2024

Type: article

Abstract: In this paper, we first present the homotopy groups of the automorphism groups of Cuntz–Krieger algebras in terms of the underlying matrices defining the Cuntz–Krieger algebras. We also show that the homotopy groups are complete invariants of the isomorphism classes of Cuntz–Krieger algebras. As a result, the isomorphism class of a Cuntz–Krieger algebra is completely determined by the group structure of its weak extension group and strong extension group.

Source: Journal of Noncommutative Geometry

DOI: 10.4171/jncg/598

Authors: Kengo Matsumoto, Taro Sogabe

Institutions: Joetsu University of Education, Kyoto University

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Japan Society for the Promotion of Science

Award: C*-algebras and its applications to classifications of orbit equivalence of symbolic dynamics and hyperbolic dynamics