Toward the classification of strongly self-absorbing $\mathrm{C}^*$-dynamical systems of compact groups

Masaki Izumi; Keiya Ohara

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arXiv · 2603.12966

Toward the classification of strongly self-absorbing $\mathrm{C}^*$-dynamical systems of compact groups

Masaki Izumi·Keiya Ohara

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Abstract

Strongly self-absorbing $\mathrm{C}^*$-algebras play a distinguished role in the classification of nuclear $\mathrm{C}^*$-algebras. Their dynamical analogues were introduced and extensively studied by Szabó. In this paper, we propose a conjecture regarding the equivariant $KK$-theory of strongly self-absorbing $\mathrm{C}^*$-dynamical systems of compact groups in the equivariant bootstrap category; an affirmative answer to this conjecture would lead to classification results. We settle this conjecture for all finite EPPO (every element has a prime-power order) groups. In the course of our proof, we establish a Künneth-type formula for the equivariant $K$-theory of $\mathrm{C}^*$-algebras equipped with finite cyclic group actions -- more precisely, for the cyclotomic part of the equivariant $K$-groups introduced by Meyer and Nadareishvili -- under a certain unique divisibility assumption.

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BibTeX RIS

Masaki Izumi, Keiya Ohara. 2026-03-13. Toward the classification of strongly self-absorbing $\mathrm{C}^*$-dynamical systems of compact groups. https://arxiv.org/abs/2603.12966

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