Geodesic
Affine Actions of Uq(sl(2)) on Polynomial Rings
Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 233-240

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DOI

We classify the affine actions of ${{U}_{q}}\left( sl\left( 2 \right) \right)$ on commutative polynomial rings in $m\,\ge \,1$ variables. We show that, up to scalar multiplication, there are two possible actions. In addition, for each action, the subring of invariants is a polynomial ring in either $m$ or $m\,-\,1$ variables, depending upon whether $q$ is or is not a root of 1.
DOI : 10.4153/CMB-2015-012-5
Mots-clés : 16T20, 17B37, 20G42, skew derivation, quantum group, invariants 
Bergen, Jeffrey. Affine Actions of Uq(sl(2)) on Polynomial Rings. Canadian mathematical bulletin, Tome 58 (2015) no. 2, pp. 233-240. doi: 10.4153/CMB-2015-012-5
@article{10_4153_CMB_2015_012_5,
     author = {Bergen, Jeffrey},
     title = {Affine {Actions} of {Uq(sl(2))} on {Polynomial} {Rings}},
     journal = {Canadian mathematical bulletin},
     pages = {233--240},
     year = {2015},
     volume = {58},
     number = {2},
     doi = {10.4153/CMB-2015-012-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-012-5/}
}
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