Centralizers in à ₂ groups

Abstract

Abstract. Let G be a torsion-free discrete group acting cocompactly on a two dimensional euclidean building D. The centralizer of an element of G is either a Bieberbach group or is described by a finite graph of finite cyclic groups. Explicit examples are computed, with D of typeà A 2 .

KMS weights on higher rank buildings

“…To search for g, we then can simply take the intersection of the space of graph weights with all edge weights equal to 1 on G 1 and on G 2 , respectively. As discussed in [15], there are exactly q + 1 faces adjacent to any given edge. Thus, each vertex (word of shape m = (m 1 , m 2 )) is the source of exactly q 2 edges with distinct ranges in G i , all of which are words of shape m + e i .…”