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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.12073 |
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| _version_ | 1866917672805990400 |
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| author | Dabrowski, Ludwik Landi, Giovanni Zanchettin, Jacopo |
| author_facet | Dabrowski, Ludwik Landi, Giovanni Zanchettin, Jacopo |
| contents | We study the relationship between antipodes on a Hopf algebroid $\mathcal{H}$ in the sense of Böhm-Szlachanyi and the group of twists that lies inside the associated convolution algebra. We specialize to the case of a faithfully flat $H$-Hopf-Galois extensions $B\subseteq A$ and related Ehresmann-Schauenburg bialgebroid. In particular, we find that the twists are in one-to-one correspondence with $H$-comodule algebra automorphism of $A$. We work out in detail the $U(1)$-extension ${\mathcal O}(\mathbb{C}P^{n-1}_q)\subseteq {\mathcal O}(S^{2n-1}_q)$ on the quantum projective space and show how to get an antipode on the bialgebroid out of the $K$-theory of the base algebra ${\mathcal O}(\mathbb{C}P^{n-1}_q)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_12073 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hopf algebroids and twists for quantum projective spaces Dabrowski, Ludwik Landi, Giovanni Zanchettin, Jacopo Quantum Algebra We study the relationship between antipodes on a Hopf algebroid $\mathcal{H}$ in the sense of Böhm-Szlachanyi and the group of twists that lies inside the associated convolution algebra. We specialize to the case of a faithfully flat $H$-Hopf-Galois extensions $B\subseteq A$ and related Ehresmann-Schauenburg bialgebroid. In particular, we find that the twists are in one-to-one correspondence with $H$-comodule algebra automorphism of $A$. We work out in detail the $U(1)$-extension ${\mathcal O}(\mathbb{C}P^{n-1}_q)\subseteq {\mathcal O}(S^{2n-1}_q)$ on the quantum projective space and show how to get an antipode on the bialgebroid out of the $K$-theory of the base algebra ${\mathcal O}(\mathbb{C}P^{n-1}_q)$. |
| title | Hopf algebroids and twists for quantum projective spaces |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2302.12073 |