## Journal of the Mathematical Society of Japan

### On representations of real Nash groups

Francesco GUARALDO

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 24 July 2012

https://projecteuclid.org/euclid.jmsj/1343133749

Digital Object Identifier
doi:10.2969/jmsj/06430927

Mathematical Reviews number (MathSciNet)
MR2965433

Zentralblatt MATH identifier
1256.14061

#### Citation

GUARALDO, Francesco. On representations of real Nash groups. J. Math. Soc. Japan 64 (2012), no. 3, 927--939. doi:10.2969/jmsj/06430927. https://projecteuclid.org/euclid.jmsj/1343133749

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