$G$-kernels of Kirchberg algebras
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913188088381440 |
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| author | Izumi, Masaki |
| author_facet | Izumi, Masaki |
| contents | A $G$-kernel is a group homomorphism from a group $G$ to the outer automorphism group of a C$^*$-algebra. Inspired by recent work of Evington and Girón Pacheco in the stably finite case, we introduce a new invariant of a $G$-kernel using $K$-theory, and deduce several new constraints of the obstruction classes of $G$-kernels in the purely infinite case. We classify $\mathbb{Z}^n$-kernels for strongly self-absorbing Kirchberg algebras in the bootstrap category in terms of our new invariant and the Dadarlat-Pennig theory of continuous fields of strongly self-absorbing C$^*$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03441 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $G$-kernels of Kirchberg algebras Izumi, Masaki Operator Algebras 46L40, 46L35, 46L55, 55N20 A $G$-kernel is a group homomorphism from a group $G$ to the outer automorphism group of a C$^*$-algebra. Inspired by recent work of Evington and Girón Pacheco in the stably finite case, we introduce a new invariant of a $G$-kernel using $K$-theory, and deduce several new constraints of the obstruction classes of $G$-kernels in the purely infinite case. We classify $\mathbb{Z}^n$-kernels for strongly self-absorbing Kirchberg algebras in the bootstrap category in terms of our new invariant and the Dadarlat-Pennig theory of continuous fields of strongly self-absorbing C$^*$-algebras. |
| title | $G$-kernels of Kirchberg algebras |
| topic | Operator Algebras 46L40, 46L35, 46L55, 55N20 |
| url | https://arxiv.org/abs/2309.03441 |