Year: 2026
Type: article
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.
Authors: KENGO MATSUMOTO, TARO SOGABE
Institutions: Joetsu University of Education, Kumamoto University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416158331
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