Quantum binary polyhedral groups and their actions on quantum planes
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We classify quantum analogues of actions of finite subgroups G of SL₂(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 2. Remarkably, the corresponding invariant rings R[superscript H] share similar regularity and Gorenstein properties as the invariant rings k[u,v] [superscript G] in the classical setting.We also present several questions and directions for expanding this work in noncommutative invariant theory.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal für die reine und angewandte Mathematik (Crelles Journal)
Walter de Gruyter
Chan, Kenneth et al. “Quantum Binary Polyhedral Groups and Their Actions on Quantum Planes.” Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2016, 719 (October 2016): 211-252 © 2016 De Gruyter
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