Totally disconnected locally compact groups with a linear open subgroup

Abstract

We describe the global structure of totally disconnected locally compact groups having a linear open compact subgroup. Among the applications, we show that if a non-discrete, compactly generated, topologically simple, totally disconnected locally compact group is locally linear, then it is a simple algebraic group over a local field.

References in corpus (8)

• Simplicity and superrigidity of twin building lattices
• Decomposing locally compact groups into simple pieces
• Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups
• Elementary totally disconnected locally compact groups
• Locally normal subgroups of totally disconnected groups. Part I: General theory
• Abstract commensurators of profinite groups
• Abstract simplicity of locally compact Kac-Moody groups
• Totally disconnected locally compact groups locally of finite rank

Cited by in corpus (4)

• Locally normal subgroups of totally disconnected groups. Part II: Compactly generated simple groups
• Locally normal subgroups of totally disconnected groups. Part I: General theory
• A classification theorem for boundary 2-transitive automorphism groups of trees
• Approximating simple locally compact groups by their dense locally compact subgroups