English

Outer automorphisms of algebraic groups and determining groups by their maximal tori

Group Theory 2015-03-12 v3 Differential Geometry Number Theory

Abstract

We give a cohomological criterion for existence of outer automorphisms of a semisimple algebraic group over an arbitrary field. This criterion is then applied to the special case of groups of type D_2n over a global field, which completes some of the main results from the paper "Weakly commensurable arithmetic groups and isospectral locally symmetric spaces" (Pub. Math. IHES, 2009) by Prasad and Rapinchuk and gives a new proof of a result from another paper by the same authors.

Keywords

Cite

@article{arxiv.1006.1298,
  title  = {Outer automorphisms of algebraic groups and determining groups by their maximal tori},
  author = {Skip Garibaldi},
  journal= {arXiv preprint arXiv:1006.1298},
  year   = {2015}
}

Comments

v2: Small changes and new title since v1 // v3: Expanded the introduction

R2 v1 2026-06-21T15:32:53.788Z