On universal property of reciprocal Kirchberg algebras and uniquely ergodic automorphisms

TL;DR

This paper establishes a universal property for reciprocal Kirchberg algebras with finitely generated K-groups and constructs a uniquely ergodic automorphism with a pure invariant state on such algebras.

Contribution

It proves a universal property for reciprocal Kirchberg algebras and demonstrates the existence of a uniquely ergodic automorphism with a pure invariant state.

Findings

Reciprocal Kirchberg algebras have a universal property related to generating subalgebras.

Existence of an aperiodic ergodic automorphism with a unique invariant state on these algebras.

The invariant state is proven to be pure.

Abstract

Reciprocality in Kirchberg algebras with finitely generated K-groups is regarded as a K-theoretic duality through K-groups and strong extension groups. We will prove that the reciprocal Kirchberg algebra has a universal property with respect to some generating C*-subalgebra and a family of generating partial isometries. By using the universal property, we will prove that there exists an aperiodic ergodic automorphism on an arbitrary unital Kirchberg algebra with finitely generated K-groups, which has a unique invariant state. The state is pure.