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Cocompact lattices in locally pro-p-complete rank 2 Kac-Moody groups
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Capdeboscq, Inna (Korchagina), Hristova, Katerina and Rumynin, Dmitriy (2020) Cocompact lattices in locally pro-p-complete rank 2 Kac-Moody groups. Matematicheskii Sbornik . (In Press)
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Abstract
We initiate an investigation of lattices in a new class of locally compact groups, so called locally pro-p-complete Kac-Moody groups. We discover that in rank 2 their cocompact lattices are particularly well-behaved: under mild assumptions, a cocompact lattice in this completion contains no elements of order p. This statement is still an open question for the Caprace-Rémy-Ronan completion. Using this, modulo results of Capdeboscq and Thomas, we classify edge-transitive cocompact lattices and describe a cocompact lattice of minimal covolume.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Kac-Moody algebras, Lattice theory, Compact groups | |||||||||
| Journal or Publication Title: | Matematicheskii Sbornik | |||||||||
| Publisher: | Steklov Mathematical Institute of Russian Academy of Sciences | |||||||||
| ISSN: | 0368-8666 | |||||||||
| Official Date: | 2020 | |||||||||
| Dates: |
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| Date of first compliant deposit: | 24 April 2020 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | In Press | |||||||||
| Publisher Statement: | `This is a preprint of the Article accepted for publication in Matematicheskii Sbornik (volume of the Journal, the year of publication). All distribution rights are owned by Steklov Mathematical Institute of Russian Academy of Sciences)’ | |||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||
| RIOXX Funder/Project Grant: |
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