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

Copyright © 2003 S. V. Ludkovsky and B. Diarra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.