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

Canadian mathematical bulletin

Jeffrey Bergen¹ 

[1] Department of Mathematics, DePaul University, 2320 N. Kenmore Avenue, Chicago, Illinois 60614, USA

关键词: skew derivation;    quantum group;    invariants;   

DOI  :  10.4153/CMB-2015-012-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We classify the affine actions of $U_q(sl(2))$ on commutativepolynomial rings in $m ge 1$ variables.We show that, up to scalar multiplication, there are two possibleactions.In addition, for each action, the subring of invariants is apolynomial ring in either $m$ or $m-1$ variables, depending upon whether $q$ is or is not a root of $1$.

【 授权许可】

Unknown