Geodesic
Quantum $s\ell(2)$ action on a~divided-power quantum plane at even
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 1, pp. 28-45

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We describe a nonstandard version of the quantum plane in which the basis is given by divided powers at an even root of unity $\mathfrak q=e^{i\pi/p}$. It can be regarded as an extension of the "nearly commutative" algebra $\mathbb C[X,Y]$ with $XY=(-1)^pYX$ 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 $\overline{\mathcal U}_{\mathfrak q}s\ell(2)$ and its Lusztig extension $\boldsymbol{\mathcal U}_{\mathfrak q}s\ell(2)$; we also define the quantum group action on the algebra of quantum differential operators on the quantum plane.
Keywords: quantum plane, divided power
Mots-clés : Lusztig quantum group, indecomposable representation. 
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     author = {A. M. Semikhatov},
     title = {Quantum $s\ell(2)$ action on a~divided-power quantum plane at even},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {28--45},
     publisher = {mathdoc},
     volume = {164},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_164_1_a1/}
}
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A. M. Semikhatov. Quantum $s\ell(2)$ action on a~divided-power quantum plane at even. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 1, pp. 28-45. http://geodesic.mathdoc.fr/item/TMF_2010_164_1_a1/