A new approach to deformation of C*-algebras via coactions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917911360176128 |
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| author | Buss, Alcides Echterhoff, Siegfried |
| author_facet | Buss, Alcides Echterhoff, Siegfried |
| contents | We revisit the procedure of deformation of $C^*$-algebras via coactions of locally compact groups and extend the methods to cover deformations for maximal, reduced, and exotic coactions for a given group $G$ and circle-valued Borel $2$-cocycles on $G$. In the special case of reduced (or normal) coactions our deformation method substantially differs from -- but turns out to be equivalent to -- the ones used by previous authors, specially those given by Bhowmick, Neshveyev, and Sangha in [7].
Our approach yields all expected results, like a good behaviour of deformations under nuclearity, continuity of fields of $C^*$-algebras and $K$-theory invariance under mild conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09997 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A new approach to deformation of C*-algebras via coactions Buss, Alcides Echterhoff, Siegfried Operator Algebras K-Theory and Homology 46L55, 22D35 We revisit the procedure of deformation of $C^*$-algebras via coactions of locally compact groups and extend the methods to cover deformations for maximal, reduced, and exotic coactions for a given group $G$ and circle-valued Borel $2$-cocycles on $G$. In the special case of reduced (or normal) coactions our deformation method substantially differs from -- but turns out to be equivalent to -- the ones used by previous authors, specially those given by Bhowmick, Neshveyev, and Sangha in [7]. Our approach yields all expected results, like a good behaviour of deformations under nuclearity, continuity of fields of $C^*$-algebras and $K$-theory invariance under mild conditions. |
| title | A new approach to deformation of C*-algebras via coactions |
| topic | Operator Algebras K-Theory and Homology 46L55, 22D35 |
| url | https://arxiv.org/abs/2305.09997 |