Affine Actions of $U_q(sl(2))$ on Polynomial Rings
Printed: Jun 2015
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
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 $1$.
skew derivation, quantum group, invariants
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]