Toward the classification of strongly self-absorbing $\mathrm{C}^*$-dynamical systems of compact groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917338783154176 |
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| author | Izumi, Masaki Ohara, Keiya |
| author_facet | Izumi, Masaki Ohara, Keiya |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12966 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Toward the classification of strongly self-absorbing $\mathrm{C}^*$-dynamical systems of compact groups Izumi, Masaki Ohara, Keiya Operator Algebras 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. |
| title | Toward the classification of strongly self-absorbing $\mathrm{C}^*$-dynamical systems of compact groups |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2603.12966 |