Submission date: 21 April 2021

Abstract:

In this paper we study groups definable in existentially closed partial differential fields of characteristic 0 with an automorphism which commutes with the derivations. In particular, we study Zariski dense definable subgroups of simple algebraic groups, and show an analogue of Phyllis Cassidy's result for partial differential fields. We also show that these groups have a smallest definable subgroup of finite index.

Mathematics Subject Classification: 03C98 (Primary), 12L12, 12H05, 12H10 (Secondary)

Keywords and phrases:

Full text arXiv 2104.10632: pdf, ps.