# Freidel-Maillet type presentations of $U_q(sl_2)$

@inproceedings{Baseilhac2021FreidelMailletTP, title={Freidel-Maillet type presentations of \$U\_q(sl\_2)\$}, author={Pascal Baseilhac}, year={2021} }

A unified framework for the Chevalley and equitable presentation of Uq(sl2) is introduced. It is given in terms of a system of Freidel-Maillet type equations satisfied by a pair of quantum K-operators K, whose entries are expressed in terms of either Chevalley or equitable generators. The Hopf algebra structure is reconsidered in light of this presentation, and interwining relations for K-operators are obtained. A Koperator solving a spectral parameter dependent Freidel-Maillet equation is also…

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## 2 Citations

On the second realization for the positive part of
$$U_q(\widehat{sl_2})$$
U
q
(

- Mathematics, PhysicsLetters in Mathematical Physics
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The equitable presentation of the quantum algebra $$U_q(\widehat{sl_2})$$ U q ( s l 2 ^ ) is considered. This presentation was originally introduced by Ito and Terwilliger. In this paper, following…

Bidiagonal Triads and the Tetrahedron Algebra

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We introduce a linear algebraic object called a bidiagonal triad. A bidiagonal triad is a modification of the previously studied and similarly defined concept of bidiagonal triple. A bidiagonal triad…

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