Cocompact lattices in locally pro- -complete rank-2 Kac-Moody groups

Inna Capdeboscq, Katerina Hristova, Dmitriy Rumynin

Type: Article

Publication Date: 2020-05-14

Citations: 0

DOI: https://doi.org/10.1070/sm9311

Abstract

Abstract We initiate an investigation of lattices in a new class of locally compact groups: so-called locally pro- <?CDATA $p$?> -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 <?CDATA $p$?> . 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. Bibliography: 22 titles.

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MPG.PuRe (Max Planck Society) - View - PDF
Warwick Research Archive Portal (University of Warwick) - View - PDF
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Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (18)

Action	Title	Year	Authors
+	Existence of discrete cocompact subgroups of reductive groups over local fields.	1978	G. Harder A. Borel
+ PDF Chat	EXISTENCE OF LATTICES IN KAC–MOODY GROUPS OVER FINITE FIELDS	2003	Lisa Carbone Howard Garland
+ PDF Chat	Simplicity and superrigidity of twin building lattices	2008	Pierre‐Emmanuel Caprace Bertrand Rémy
+	Uniqueness and presentation of Kac-Moody groups over fields	1987	Jacques Tits
+ PDF Chat	Co-compact lattices in complete Kac-Moody groups with Weyl group right-angled or a free product of spherical special subgroups	2013	Inna Capdeboscq Anne Thomas
+	Automorphisms of Affine Kac-Moody Groups and Related Chevalley Groups over Rings	1993	R.W. Carter Y. Chen
+ PDF Chat	Abstract simplicity of complete Kac–Moody groups over finite fields	2008	Lisa Carbone Mikhail Ershov Gordon Ritter
+	Lattices in complete rank 2 Kac–Moody groups	2011	Inna Capdeboscq Anne Thomas
+	Torsion elements and centralizers in free products of profinite groups.	1985	Wolfgang Herfort Luis Ribes
+	Some Remarks on Discontinuous Groups	1945	Carl Ludwig Siegel