Cocompact Lattices in Locally Pro-p-complete Rank 2 Kac-Moody Groups

2018/07/20 by Inna Capdeboscq, Capdeboscq, Inna, Katerina Hristova +3
Mathematics · #20G44 (primary) #22E40 (secondary) #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1807.07929

openalex publication_date 2018/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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