Automorphisms of partially commutative groups I: Linear subgroups

作者：Duncan Andrew J^*; Kazachkov Ilya V; Remeslennikov Vladimir N

来源：Groups, Geometry, and Dynamics, 2010, 4(4): 739-757.

DOI：10.4171/GGD/103

• Partially commutative groups
• right-angled Artin groups
• automorphism groups
• arithmetic groups

We construct and describe several arithmetic subgroups of the automorphism group of a partially commutative group. More precisely, given an arbitrary finite graph Gamma we construct arithmetic subgroups St(LY) and St(L(max)), represented as subgroups of GL(n, Z), where n is the number of vertices of the graph Gamma. Here L(Y) and L(max) are certain lattices of subsets of X = V(Gamma) and St(K) is the stabiliser of the subgroup generated by K. In addition we give a description of the decomposition of the group St(conj)(L(X)), which stabilises LX up to conjugacy, as a semidirect product of the group of conjugating automorphisms and St(L(X)).

• 出版日期2010