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Affine Actions of $U_q(sl(2))$ on Polynomial Rings

  Published:2015-03-09
 Printed: Jun 2015
  • Jeffrey Bergen,
    Department of Mathematics, DePaul University, 2320 N. Kenmore Avenue, Chicago, Illinois 60614, USA
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Abstract

We classify the affine actions of $U_q(sl(2))$ 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 $1$.
Keywords: skew derivation, quantum group, invariants skew derivation, quantum group, invariants
MSC Classifications: 16T20, 17B37, 20G42 show english descriptions Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]
Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]
16T20 - Ring-theoretic aspects of quantum groups [See also 17B37, 20G42, 81R50]
17B37 - Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
20G42 - Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]
 

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