A structure and representations of diffeomorphism groups of non-Archimedean manifolds

Details A structure and representations of diffeomorphism groups of non-Archimedean manifolds A structure and representations of diffeomorphism groups of non-Archimedean manifolds

2000-04-19

arxiv.org/abs/math/0004126v1

Mathematics

Group Theory

32 pages, Latex

Scientific paper

Diffeomorphism groups $G$ of manifolds $M$ on locally $\bf F$-convex spaces over non-Archimedean fields $\bf F$ are investigated. It is shown that their structure has many differences with the diffeomorphism groups of real and complex manifolds. It is proved that $G$ is not a Banach-Lie group, but it has a neighbourhood $W$ of the unit element $e$ such that each element $g$ in $W$ belongs to at least one corresponding one-parameter subgroup. It is proved that $G$ is simple and perfect. Its compact subgroups $G_c$ are studied such that a dimension over $\bf F$ of its tangent space $dim_{\bf F}T_eG_c$ in $e$ may be infinite. This is used for decompositions of continuous representations into irreducible and investigations of induced representations.

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