### On representations of real Nash groups

Francesco GUARALDO
Source: J. Math. Soc. Japan Volume 64, Number 3 (2012), 927-939.

#### Abstract

Some basic results on compact affine Nash groups related to their Nash representations are given. So, first a Nash version of the Peter-Weil theorem is proved and then several more results are given: for example, it is proved that an analytic representation of such a group is of class Nash and that the category of the classes of isomorphic embedded compact Nash groups is isomorphic with that of the classes of isomorphic embedded algebraic groups. Moreover, given a compact affine Nash group G, a closed subgroup H and a homogeneous Nash G-manifold X, it is proved that the twisted product G ×H X is a Nash G-manifold which is Nash G-diffeomorphic to an algebraic G-variety; besides, this algebraic structure is unique.

First Page:
Primary Subjects: 20G05
Secondary Subjects: 57S15, 14P20
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Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1343133749
Digital Object Identifier: doi:10.2969/jmsj/06430927
Zentralblatt MATH identifier: 06090098
Mathematical Reviews number (MathSciNet): MR2965433

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