Quantum binary polyhedral groups and their actions on quantum planes
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 a...
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Walter de Gruyter
2017
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| Online Access: | http://hdl.handle.net/1721.1/112271 |
| _version_ | 1811093083373174784 |
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| author | Walton, Chelsea |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Walton, Chelsea |
| author_sort | Walton, Chelsea |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T15:39:26Z |
| format | Article |
| id | mit-1721.1/112271 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T15:39:26Z |
| publishDate | 2017 |
| publisher | Walter de Gruyter |
| record_format | dspace |
| spelling | mit-1721.1/1122712022-10-02T03:13:31Z Quantum binary polyhedral groups and their actions on quantum planes Walton, Chelsea Massachusetts Institute of Technology. Department of Mathematics Walton, Chelsea 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. National Science Foundation (U.S.) (Grant DMS-1102548) National Science Foundation (U.S.) (Grant DMS-0855743) 2017-11-22T14:54:11Z 2017-11-22T14:54:11Z 2014-07 2017-10-27T17:19:39Z Article http://purl.org/eprint/type/JournalArticle 0075-4102 1435-5345 http://hdl.handle.net/1721.1/112271 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 http://dx.doi.org/10.1515/crelle-2014-0047 Journal für die reine und angewandte Mathematik (Crelles Journal) 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. application/pdf Walter de Gruyter De Gruyter |
| spellingShingle | Walton, Chelsea Quantum binary polyhedral groups and their actions on quantum planes |
| title | Quantum binary polyhedral groups and their actions on quantum planes |
| title_full | Quantum binary polyhedral groups and their actions on quantum planes |
| title_fullStr | Quantum binary polyhedral groups and their actions on quantum planes |
| title_full_unstemmed | Quantum binary polyhedral groups and their actions on quantum planes |
| title_short | Quantum binary polyhedral groups and their actions on quantum planes |
| title_sort | quantum binary polyhedral groups and their actions on quantum planes |
| url | http://hdl.handle.net/1721.1/112271 |
| work_keys_str_mv | AT waltonchelsea quantumbinarypolyhedralgroupsandtheiractionsonquantumplanes |