Mystic Reflection Groups
This paper aims to systematically study mystic reflection groups that emerged independently in the paper [Selecta Math. (N.S.) 14 (2009), 325-372] by the authors and in the paper [Algebr. Represent. Theory 13 (2010), 127-158] by Kirkman, Kuzmanovich and Zhang. A detailed analysis of this class of gr...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2014 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146818 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Mystic Reflection Groups / Y. Bazlov, A. Berenstein // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 2 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862552155969290240 |
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| author | Bazlov, Y. Berenstein, A. |
| author_facet | Bazlov, Y. Berenstein, A. |
| citation_txt | Mystic Reflection Groups / Y. Bazlov, A. Berenstein // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 2 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This paper aims to systematically study mystic reflection groups that emerged independently in the paper [Selecta Math. (N.S.) 14 (2009), 325-372] by the authors and in the paper [Algebr. Represent. Theory 13 (2010), 127-158] by Kirkman, Kuzmanovich and Zhang. A detailed analysis of this class of groups reveals that they are in a nontrivial correspondence with the complex reflection groups G(m,p,n). We also prove that the group algebras of corresponding groups are isomorphic and classify all such groups up to isomorphism.
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| first_indexed | 2025-11-25T21:04:10Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146818 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T21:04:10Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bazlov, Y. Berenstein, A. 2019-02-11T16:21:38Z 2019-02-11T16:21:38Z 2014 Mystic Reflection Groups / Y. Bazlov, A. Berenstein // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 2 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 16G99; 20F55; 16S80 DOI:10.3842/SIGMA.2014.040 https://nasplib.isofts.kiev.ua/handle/123456789/146818 This paper aims to systematically study mystic reflection groups that emerged independently in the paper [Selecta Math. (N.S.) 14 (2009), 325-372] by the authors and in the paper [Algebr. Represent. Theory 13 (2010), 127-158] by Kirkman, Kuzmanovich and Zhang. A detailed analysis of this class of groups reveals that they are in a nontrivial correspondence with the complex reflection groups G(m,p,n). We also prove that the group algebras of corresponding groups are isomorphic and classify all such groups up to isomorphism. This paper is a contribution to the Special Issue in honor of Anatol Kirillov and Tetsuji Miwa. The full
 collection is available at http://www.emis.de/journals/SIGMA/InfiniteAnalysis2013.html.
 We thank Ken Brown for bringing the paper [2] to our attention, and Alexander Premet for
 stimulating discussions. The present paper was started when both authors were research members
 of the Mathematical Sciences Research Institute. We thank the Institute and the organizers
 of the Noncommutative Algebraic Geometry and Representation Theory program for creating
 an atmosphere conducive for research. We acknowledge partial support of the LMS Research
 in Pairs grant ref. 41224. The second named author was partially supported by the NSF grant
 DMS-1101507. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Mystic Reflection Groups Article published earlier |
| spellingShingle | Mystic Reflection Groups Bazlov, Y. Berenstein, A. |
| title | Mystic Reflection Groups |
| title_full | Mystic Reflection Groups |
| title_fullStr | Mystic Reflection Groups |
| title_full_unstemmed | Mystic Reflection Groups |
| title_short | Mystic Reflection Groups |
| title_sort | mystic reflection groups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146818 |
| work_keys_str_mv | AT bazlovy mysticreflectiongroups AT berensteina mysticreflectiongroups |