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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/2303.02228 |
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| _version_ | 1866914939053015040 |
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| author | Andruskiewitsch, Nicolás Bagio, Dirceu Della Flora, Saradia Flôres, Daiana |
| author_facet | Andruskiewitsch, Nicolás Bagio, Dirceu Della Flora, Saradia Flôres, Daiana |
| contents | We consider the restricted Jordan plane in characteristic $2$, a finite-dimensional Nichols algebra quotient of the Jordan plane that was introduced by Cibils, Lauve and Witherspoon. We extend results from \texttt{arXiv:2002.02514} on the analogous object in odd characteristic. We show that the Drinfeld double of the restricted Jordan plane fits into an exact sequence of Hopf algebras whose kernel is a normal local commutative Hopf subalgebra and the cokernel is the restricted enveloping algebra of a restricted Lie algebra $\mathfrak m$ of dimension 5. We show that $\mathfrak u(\mathfrak m)$ is tame and compute explicitly the indecomposable modules. An infinite-dimensional Hopf algebra covering the Drinfeld double of the restricted Jordan plane is introduced. Various quantum Frobenius maps are described. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02228 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Drinfeld double of the restricted Jordan plane in characteristic $2$ Andruskiewitsch, Nicolás Bagio, Dirceu Della Flora, Saradia Flôres, Daiana Quantum Algebra We consider the restricted Jordan plane in characteristic $2$, a finite-dimensional Nichols algebra quotient of the Jordan plane that was introduced by Cibils, Lauve and Witherspoon. We extend results from \texttt{arXiv:2002.02514} on the analogous object in odd characteristic. We show that the Drinfeld double of the restricted Jordan plane fits into an exact sequence of Hopf algebras whose kernel is a normal local commutative Hopf subalgebra and the cokernel is the restricted enveloping algebra of a restricted Lie algebra $\mathfrak m$ of dimension 5. We show that $\mathfrak u(\mathfrak m)$ is tame and compute explicitly the indecomposable modules. An infinite-dimensional Hopf algebra covering the Drinfeld double of the restricted Jordan plane is introduced. Various quantum Frobenius maps are described. |
| title | On the Drinfeld double of the restricted Jordan plane in characteristic $2$ |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2303.02228 |