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

I. Capdeboscq, K. Hristova, D. A. Rumynin

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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. Bibliography: 22 titles.

Original languageEnglish
Pages (from-to)1065-1079
Number of pages15
JournalSbornik: Mathematics
Volume211
Issue number8
DOIs
Publication statusPublished - Aug 2020

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