Dual coalgebras of twisted tensor products
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915106231681024 |
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| author | Reyes, Manuel L. |
| author_facet | Reyes, Manuel L. |
| contents | We investigate cases where the finite dual coalgebra of a twisted tensor product of two algebras is a cotwisted tensor product of their respective finite dual coalgebras. This is achieved by interpreting the finite dual as a topological dual; in order to prove this, we show that the continuous dual is a strong monoidal functor on linearly topologized vector spaces whose open subspaces have finite codimension. We describe a sufficient condition for the result on finite dual coalgebras to be applied, and we this condition to particular constructions including Ore extensions, smash product algebras, and crossed product bialgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_17261 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dual coalgebras of twisted tensor products Reyes, Manuel L. Rings and Algebras Category Theory Primary: 16S35, 16T15, 18M05, Secondary: 16S38, 16S40, 16S80 We investigate cases where the finite dual coalgebra of a twisted tensor product of two algebras is a cotwisted tensor product of their respective finite dual coalgebras. This is achieved by interpreting the finite dual as a topological dual; in order to prove this, we show that the continuous dual is a strong monoidal functor on linearly topologized vector spaces whose open subspaces have finite codimension. We describe a sufficient condition for the result on finite dual coalgebras to be applied, and we this condition to particular constructions including Ore extensions, smash product algebras, and crossed product bialgebras. |
| title | Dual coalgebras of twisted tensor products |
| topic | Rings and Algebras Category Theory Primary: 16S35, 16T15, 18M05, Secondary: 16S38, 16S40, 16S80 |
| url | https://arxiv.org/abs/2306.17261 |