Quantum binary polyhedral groups and their actions on quantum planes
Quantum binary polyhedral groups and their actions on quantum planes
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DOI：
10.1515/crelle-2014-0047
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发表时间：
2013-03
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通讯作者：
K. Chan;E. Kirkman;Chelsea M. Walton;James J. Zhang
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文献类型：
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作者：
K. Chan;E. Kirkman;Chelsea M. Walton;James J. Zhang
本文对SL_2（k）的有限子群G在交换多项式环k[u，v]上作用的量子模拟进行了分类。更确切地说，我们产生一个分类对（H，R），其中H是一个有限维的Hopf代数，行为内部忠实，并保持了评分的Artin-Schelter正则代数R的全球维度2。值得注意的是，对应的不变环R^H与经典情形下的不变环k[u，v]^G具有相似的正则性和Gorenstein性质。我们还提出了几个问题和方向，扩大这项工作的非交换不变理论。
We classify quantum analogues of actions of finite subgroups G of SL_2(k) on commutative polynomial rings k[u,v]. More precisely, we produce a classification of pairs (H,R), where H is a finite dimensional Hopf algebra that acts inner faithfully and preserves the grading of an Artin-Schelter regular algebra R of global dimension two. Remarkably, the corresponding invariant rings R^H share similar regularity and Gorenstein properties as the invariant rings k[u,v]^G in the classic setting. We also present several questions and directions for expanding this work in noncommutative invariant theory.