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July, 2012 On representations of real Nash groups
Francesco GUARALDO
J. Math. Soc. Japan 64(3): 927-939 (July, 2012). DOI: 10.2969/jmsj/06430927


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.


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Francesco GUARALDO. "On representations of real Nash groups." J. Math. Soc. Japan 64 (3) 927 - 939, July, 2012.


Published: July, 2012
First available in Project Euclid: 24 July 2012

zbMATH: 1256.14061
MathSciNet: MR2965433
Digital Object Identifier: 10.2969/jmsj/06430927

Primary: 20G05
Secondary: 14P20 , 57S15

Keywords: equivariant Nash conjecture , representation theory

Rights: Copyright © 2012 Mathematical Society of Japan


Vol.64 • No. 3 • July, 2012
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