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Affine Actions of Uq(sl(2)) on Polynomial Rings
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2015