International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 42, Pages 2673-2688
Profinite and finite groups associated with loop and diffeomorphism groups of non-Archimedean manifolds
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.
We investigate -adic completions of clopen (i.e., closed and open at the same time) subgroups of loop groups and diffeomorphism groups 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.