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Capdeboscq, Inna, Rumynin, Dmitriy and Kirkina, Karina (2018) Presentations of Affine Kac-Moody groups. Forum of Mathematics, Sigma, 6 . e21. doi:10.1017/fms.2018.19 ISSN 2050-5094.
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Official URL: https://doi.org/10.1017/fms.2018.19
Abstract
How many generators and relations does SL n ( F q [ t , t − 1 ] ) need? In this paper we exhibit its explicit presentation with 9 generators and 44 relations. We investigate presentations of affine Kac–Moody groups over finite fields. Our goal is to derive finite presentations, independent of the field and with as few generators and relations as we can achieve. It turns out that any simply connected affine Kac–Moody group over a finite field has a presentation with at most 11 generators and 70 relations. We describe these presentations explicitly type by type. As a consequence, we derive explicit presentations of Chevalley groups G ( F q [ t , t − 1 ] ) and explicit profinite presentations of profinite Chevalley groups G ( F q [[ t ]] ) .
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Kac-Moody algebras, Affine algebraic groups | |||||||||
| Journal or Publication Title: | Forum of Mathematics, Sigma | |||||||||
| Publisher: | Cambridge University Press | |||||||||
| ISSN: | 2050-5094 | |||||||||
| Official Date: | 26 October 2018 | |||||||||
| Dates: |
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| Volume: | 6 | |||||||||
| Article Number: | e21 | |||||||||
| DOI: | 10.1017/fms.2018.19 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 26 July 2018 | |||||||||
| Date of first compliant Open Access: | 19 December 2018 | |||||||||
| RIOXX Funder/Project Grant: |
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