Hopfological invariants for tame subextensions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929723990343680 |
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| author | Ohara, Mariko |
| author_facet | Ohara, Mariko |
| contents | Let H be a finite dimensional Hopf algebra over a field K. In this paper, we study when an H-extension becomes a tame H-extension by calculating Hopfological homology and Hopf-cyclic homology. In the (derived) category of H'-comodules for a Hopf algebra H', we take Hopf subalgebra H of H' and a certain order A of H. We see the behavior of Hopfological homology for a tame A-subextension S/R in terms of the surjectivity of trace map and of cyclic modules, which induce Hopf-cyclic homology, for Hopf-Galois extensions with H in terms of relative Hopf modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15191 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hopfological invariants for tame subextensions Ohara, Mariko K-Theory and Homology Quantum Algebra 16T15, 18G20, 57T0, 55N25 Let H be a finite dimensional Hopf algebra over a field K. In this paper, we study when an H-extension becomes a tame H-extension by calculating Hopfological homology and Hopf-cyclic homology. In the (derived) category of H'-comodules for a Hopf algebra H', we take Hopf subalgebra H of H' and a certain order A of H. We see the behavior of Hopfological homology for a tame A-subextension S/R in terms of the surjectivity of trace map and of cyclic modules, which induce Hopf-cyclic homology, for Hopf-Galois extensions with H in terms of relative Hopf modules. |
| title | Hopfological invariants for tame subextensions |
| topic | K-Theory and Homology Quantum Algebra 16T15, 18G20, 57T0, 55N25 |
| url | https://arxiv.org/abs/2502.15191 |