Tensor category equivariant KK-theory
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915202136539136 |
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| author | Arano, Yuki Kitamura, Kan Kubota, Yosuke |
| author_facet | Arano, Yuki Kitamura, Kan Kubota, Yosuke |
| contents | In this paper, we introduce Kasparov's bivariant K-theory that is equivariant under symmetries of a C*-tensor category. It is motivated by some dualities in quantum group equivariant KK-theory, and the classification theory of inclusions of C*-algebras. The fundamental properties of the KK-theory, i.e., the existence of the Kasparov product, Cuntz's picture, universality, and triangulated category structure, hold true in this generalization as well. Moreover, we further prove a new property specific to this theory; the invariance of KK-theory under weak Morita equivalence of the tensor categories. As an example, we study the Baum-Connes type property for $3$-cocycle twists of discrete groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_07255 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tensor category equivariant KK-theory Arano, Yuki Kitamura, Kan Kubota, Yosuke Operator Algebras K-Theory and Homology Primary 19K35, Secondary 20G42, 46L35 In this paper, we introduce Kasparov's bivariant K-theory that is equivariant under symmetries of a C*-tensor category. It is motivated by some dualities in quantum group equivariant KK-theory, and the classification theory of inclusions of C*-algebras. The fundamental properties of the KK-theory, i.e., the existence of the Kasparov product, Cuntz's picture, universality, and triangulated category structure, hold true in this generalization as well. Moreover, we further prove a new property specific to this theory; the invariance of KK-theory under weak Morita equivalence of the tensor categories. As an example, we study the Baum-Connes type property for $3$-cocycle twists of discrete groups. |
| title | Tensor category equivariant KK-theory |
| topic | Operator Algebras K-Theory and Homology Primary 19K35, Secondary 20G42, 46L35 |
| url | https://arxiv.org/abs/2305.07255 |