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arXiv · 0901.1478

Quantum-sl(2) action on a divided-power quantum plane at even roots of unity

AM Semikhatov
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Abstract

We describe a nonstandard version of the quantum plane, the one in the basis of divided powers at an even root of unity $q=e^{i\pi/p}$. It can be regarded as an extension of the "nearly commutative" algebra $C[X,Y]$ with $X Y =(-1)^p Y X$ by nilpotents. For this quantum plane, we construct a Wess--Zumino-type de Rham complex and find its decomposition into representations of the $2p^3$-dimensional quantum group $U_q sl(2)$ and its Lusztig extension; the quantum group action is also defined on the algebra of quantum differential operators on the quantum plane.

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AM Semikhatov. 2009-01-11. Quantum-sl(2) action on a divided-power quantum plane at even roots of unity. https://doi.org/10.1007/s11232-010-0068-5

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