Journal of the Australian Mathematical Society· 2026Q2
ON UNIVERSAL PROPERTY OF RECIPROCAL KIRCHBERG ALGEBRAS AND UNIQUELY ERGODIC AUTOMORPHISMS
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- Q2SCImago
- 2026year
Short summary
A reciprocal Kirchberg algebra with finitely generated K-groups possesses a universal property related to its generating C*-subalgebra and partial isometries, enabling the proof of an aperiodic, uniquely ergodic automorphism with a pure invariant state.
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Key points
- Reciprocal Kirchberg algebras with finitely generated K-groups exhibit a universal property concerning generating C*-subalgebras and partial isometries.
- This universal property is leveraged to prove the existence of an aperiodic ergodic automorphism.
- The proven automorphism is uniquely ergodic, possessing a single invariant state.
- The invariant state associated with this automorphism is pure.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract Reciprocality in Kirchberg algebras with finitely generated K $\mathrm {K}$ normal upper K -groups is regarded as a K $\mathrm {K}$ normal upper K -theoretic duality through K $\mathrm {K}$ normal upper K -groups and strong extension groups. We prove that the reciprocal Kirchberg algebra has a universal property with respect to some generating C ∗ $C^*$ upper C Superscript asterisk -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 K $\mathrm {K}$ normal upper K -groups, which has a unique invariant state. The state is pure.
The authors' abstract, as published at the source. Journal of the Australian Mathematical Society, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics