Quantum binary polyhedral groups and their actions on quantum planes
Name
Chan-2016-EMB UNTIL Oct 1, 2017 Quantum binary polyhedral groups and.pdf
Size
513.6 KB
Format
Adobe PDF
Checksum (MD5)
150dd930e0ea0735280a3fa3980cddf0
Author(s)
Walton, Chelsea
Date Issued
July 2014
Journal
Journal für die reine und angewandte Mathematik (Crelles Journal)
Publisher
Walter de Gruyter
Citation
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
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1515/crelle-2014-0047
