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2015•Canadian Mathematical BulletinOpen access

Affine Actions of Uq(sl(2)) on Polynomial Rings

Jeffrey Bergen

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Abstract

Abstract We classify the affine actions of Uq(sl(2)) on commutative polynomial rings in m ≥ 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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Abstract We classify the affine actions of Uq(sl(2)) on commutative polynomial rings in m ≥ 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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Abstract We classify the affine actions of Uq(sl(2)) on commutative polynomial rings in m ≥ 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.

Key concepts: Subring, Mathematics, Polynomial ring, Affine transformation, Polynomial, Commutative ring, Commutative property, Discrete mathematics

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