Multiplicities and dimensions in enveloping tensor categories
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912182368731136 |
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| author | Knop, Friedrich |
| author_facet | Knop, Friedrich |
| contents | In the previous paper arxiv:math/0610552 semisimple tensor categories were constructed out of certain regular Mal'cev categories. In this paper, we calculate the tensor product multiplicities and the categorical dimensions of the simple objects. This yields also the Grothendieck ring. The main tool is the subquotient decomposition of the basic objects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_10337 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Multiplicities and dimensions in enveloping tensor categories Knop, Friedrich Category Theory Representation Theory 17B22, 14L30, 11F70 In the previous paper arxiv:math/0610552 semisimple tensor categories were constructed out of certain regular Mal'cev categories. In this paper, we calculate the tensor product multiplicities and the categorical dimensions of the simple objects. This yields also the Grothendieck ring. The main tool is the subquotient decomposition of the basic objects. |
| title | Multiplicities and dimensions in enveloping tensor categories |
| topic | Category Theory Representation Theory 17B22, 14L30, 11F70 |
| url | https://arxiv.org/abs/2209.10337 |