$\mathfrak{R}$-matrix for quantum superalgebra $\mathfrak{sl}(2|1)$ at roots of unity and its application to centralizer algebras

Alexander Mazurenko; Vladimir A. Stukopin

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arXiv · 1909.11613

$\mathfrak{R}$-matrix for quantum superalgebra $\mathfrak{sl}(2|1)$ at roots of unity and its application to centralizer algebras

Alexander Mazurenko·Vladimir A. Stukopin

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Abstract

We consider fundamental facts from the theory of Hopf superalgebras. We use them to construct the quantum double of the quantum superalgebra $sl(2|1)$ at roots of unity. Thus we obtain a multiplicative formula for universal $R$-matrix. Next we construct an $R$-matrix to investigate parametrized family of centralizer algebras. We give multiplication laws in particular case and describe a structure of such algebras in the general case.

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Alexander Mazurenko, Vladimir A. Stukopin. 2019-09-25. $\mathfrak{R}$-matrix for quantum superalgebra $\mathfrak{sl}(2|1)$ at roots of unity and its application to centralizer algebras. https://arxiv.org/abs/1909.11613

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