The Chern-Weil homomorphism for deformed Hopf-Galois extensions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911032544329728 |
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| author | Zanchettin, Jacopo |
| author_facet | Zanchettin, Jacopo |
| contents | In this article, we study the Chern-Weil theory for Hopf-Galois extensions originally introduced by Hajac and Maszczyk in the context of coalgebra extensions. We show that the cyclic homology Chern-Weil homomorphism defines natural transformations between Hopf-Galois extensions with a strong connection (principal comodule algebras) and cyclic homology, thereby generalizing the concept of characteristic classes to the noncommutative setting. In the second part, we study the effect of $2$-cocycle deformations of Hopf-Galois extensions on the aforementioned homomorphism. We consider the $2$-cocycle coming from the structure Hopf algebra of the extension, an external symmetry, and finally the combined case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12927 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Chern-Weil homomorphism for deformed Hopf-Galois extensions Zanchettin, Jacopo Quantum Algebra In this article, we study the Chern-Weil theory for Hopf-Galois extensions originally introduced by Hajac and Maszczyk in the context of coalgebra extensions. We show that the cyclic homology Chern-Weil homomorphism defines natural transformations between Hopf-Galois extensions with a strong connection (principal comodule algebras) and cyclic homology, thereby generalizing the concept of characteristic classes to the noncommutative setting. In the second part, we study the effect of $2$-cocycle deformations of Hopf-Galois extensions on the aforementioned homomorphism. We consider the $2$-cocycle coming from the structure Hopf algebra of the extension, an external symmetry, and finally the combined case. |
| title | The Chern-Weil homomorphism for deformed Hopf-Galois extensions |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2312.12927 |