Representations of $\bar{U}_q s\ell(2|1)$ at even roots of unity
| Autor: | Semikhatov, A M, Tipunin, I Yu |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | J. Math. Phys. 57, 021707 (2016) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.4940661 |
| Popis: | We construct all projective modules of the restricted quantum group $\bar{U}_q s\ell(2|1)$ at an even, $2p$th, root of unity. This $64p^4$-dimensional Hopf algebra is a common double bosonization, $B(X^*)\otimes B(X)\otimes H$, of two rank-2 Nichols algebras $B(X)$ with fermionic generator(s), with $H=Z_{2p}\otimes Z_{2p}$. The category of $\bar{U}_q s\ell(2|1)$-modules is equivalent to the category of Yetter--Drinfeld $B(X)$-modules in $C_{\rho}={}^H_H\!YD$, where coaction is defined by a universal $R$-matrix $\rho$. As an application of the projective module construction, we find the associative algebra structure and the dimension, $5p^2-p+4$, of the $\bar{U}_q s\ell(2|1)$ center. Comment: 55 pp, amsart + xy + mathabx + t-angles + |
| Databáze: | arXiv |
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