Geodesic
Equivariant Embeddings of Differentiable Spaces
Serdica Mathematical Journal, Tome 27 (2001) no. 2, pp. 107-114.

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Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).
Keywords: Affine Differentiable Spaces, Actions of Compact Lie Groups, Differentiable Algebras 
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     author = {Rivas, R. and Gonz\'alez, J. and De Salas, J.},
     title = {Equivariant {Embeddings} of {Differentiable} {Spaces}},
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Rivas, R.; González, J.; De Salas, J. Equivariant Embeddings of Differentiable Spaces. Serdica Mathematical Journal, Tome 27 (2001) no. 2, pp. 107-114. http://geodesic.mathdoc.fr/item/SMJ2_2001_27_2_a1/