Additive C*-categories and K-theory
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866911310960132096 |
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| author | Bunke, Ulrich Engel, Alexander |
| author_facet | Bunke, Ulrich Engel, Alexander |
| contents | We review the notions of a multiplier category and the $W^{*}$-envelope of a $C^{*}$-category. We then consider the notion of an orthogonal sum of a (possibly infinite) family of objects in a $C^{*}$-category. Furthermore, we construct reduced crossed products of $C^{*}$-categories with groups. We axiomatize the basic properties of the $K$-theory for $C^{*}$-categories in the notion of a homological functor. We then study various rigidity properties of homological functors in general, and special additional features of the $K$-theory of $C^{*}$-categories. As an application we construct and study interesting functors on the orbit category of a group from $C^{*}$-categorical data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_14830 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Additive C*-categories and K-theory Bunke, Ulrich Engel, Alexander K-Theory and Homology Algebraic Topology Operator Algebras We review the notions of a multiplier category and the $W^{*}$-envelope of a $C^{*}$-category. We then consider the notion of an orthogonal sum of a (possibly infinite) family of objects in a $C^{*}$-category. Furthermore, we construct reduced crossed products of $C^{*}$-categories with groups. We axiomatize the basic properties of the $K$-theory for $C^{*}$-categories in the notion of a homological functor. We then study various rigidity properties of homological functors in general, and special additional features of the $K$-theory of $C^{*}$-categories. As an application we construct and study interesting functors on the orbit category of a group from $C^{*}$-categorical data. |
| title | Additive C*-categories and K-theory |
| topic | K-Theory and Homology Algebraic Topology Operator Algebras |
| url | https://arxiv.org/abs/2010.14830 |