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ON UNIVERSAL PROPERTY OF RECIPROCAL KIRCHBERG ALGEBRAS AND UNIQUELY ERGODIC AUTOMORPHISMS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 18 September 2026, pp. 1-30
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- Article
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Reciprocality in Kirchberg algebras with finitely generated $\mathrm {K}$
-groups is regarded as a $\mathrm {K}$
-theoretic duality through $\mathrm {K}$
-groups and strong extension groups. We 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 prove that there exists an aperiodic ergodic automorphism on an arbitrary unital Kirchberg algebra with finitely generated $\mathrm {K}$
-groups, which has a unique invariant state. The state is pure.
