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arXiv · 1911.01011

Drinfeld double of deformed quantum algebras

Zhaobing Fan·Junjing Xing
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Abstract

We provide a deformation, $\mathfrak{f}_{\beta}$, of Lusztig algebra $\mathbf{f}$. Various quantum algebras in literatures, including half parts of two-parameter quantum algebras, quantum superalgebras, and multi-parameter quantum algebras/superalgebras, are all specializations of $\mathfrak{f}_{\beta}$. Moreover, $\mathfrak{f}_{\beta}$ is isomorphic to Lusztig algebra $\mathbf{f}$ up to a twist. As a consequence, half parts of those quantum algebras are isomorphic to Lusztig algebra $\mathbf{f}$ over a big enough ground field up to certain twists. We further construct the entire algebra $\mathbf U_{\beta,\xi}$ by Drinfeld double construction. As special cases, above quantum algebras all admit a Drinfeld double construction under certain assumptions.

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BibTeXRIS

Zhaobing Fan, Junjing Xing. 2019-11-04. Drinfeld double of deformed quantum algebras. https://doi.org/10.1016/j.jalgebra.2019.05.036

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