On strong extension groups of Cuntz--Krieger algebras

TL;DR

This paper investigates the structure of strong extension groups of Cuntz--Krieger algebras, providing a formula for computation and analyzing the role of Toeplitz extensions in classifying these algebras.

Contribution

It introduces a formula for calculating strong extension groups and identifies the position of Toeplitz extensions as a key invariant for classification.

Findings

Derived a formula to compute strong extension groups.

Identified the position of Toeplitz extension as a complete invariant.

Connected weak extension groups with algebra isomorphism classification.

Abstract

In this paper, we study the strong extension groups of Cuntz--Krieger algebras, and present a formula to compute the groups. We also detect the position of the Toeplitz extension of a Cuntz--Krieger algebra in the strong extension group and in the weak extension group to see that the weak extension group with the position of the Toeplitz extension is a complete invariant of the isomorphism class of the Cuntz--Krieger algebra associated with its transposed matrix.