Abstract
In [7] the $q$ tetrahedron algebra $\boxtimes_{q}$ was introduced as a $q$ analogue of the universal enveloping algebra of the three point loop algebra $\mathit{sl}_{2} \otimes \mathbf{C}[t,t^{-1},(t-1)^{-1}]$. In this paper the relation between finite dimensional $\boxtimes_{q}$ modules and finite dimensional modules for $U_{q}(L(\mathit{sl}_{2}))$, a $q$ analogue of the loop algebra $L(\mathit{sl}_{2})$, is studied. A connection between the $\boxtimes_{q}$ module structure and $L$-operators for $U_{q}(L(\mathit{sl}_{2}))$ is also discussed.
Citation
Kei Miki. "Finite dimensional modules for the $q$-tetrahedron algebra." Osaka J. Math. 47 (2) 559 - 589, June 2010.
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