International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 42, Pages 2673-2688
doi:10.1155/S0161171203011499

Profinite and finite groups associated with loop and diffeomorphism groups of non-Archimedean manifolds

S. V. Ludkovsky1 and B. Diarra1

 1Theoretical Department, Institute of General Physics, Russian Academy of Sciences, 38 Street Vavilov, Moscow 119991, GSP-1, Russia
2Département de Mathématiques, Laboratoire de Mathématiques Pures, Complexe Scientifique des Cézeaux, Aubiére Cedex 63177, France
Received 22 January 2001; Revised 15 June 2001

Abstract

We investigate p-adic completions of clopen (i.e., closed and open at the same time) subgroups W of loop groups and diffeomorphism groups G of compact manifolds over non-Archimedean fields. We outline two different compactifications of loop groups and one compactification of diffeomorphism groups, describe associated finite groups in projective limits, and discuss relations with the representation theory.