Geodesic
Equivariant compactifications of reductive groups
Sbornik. Mathematics, Tome 194 (2003) no. 4, pp. 589-616 Cet article a éte moissonné depuis la source Math-Net.Ru

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Under study are equivariant projective compactifications of reductive groups that can be obtained as the closure of the image of the group in the space of projective linear operators of a representation. The structure and the mutual position of the orbits of the action of the direct square of the group acting by left/right multiplication and the local structure of the compactification in the neighbourhood of a closed orbit are described. Several conditions for the normality and smoothness of a compactification are obtained. The methods used are based on the theory of equivariant embeddings of spherical homogeneous spaces and reductive algebraic semigroups. 
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D. A. Timashev. Equivariant compactifications of reductive groups. Sbornik. Mathematics, Tome 194 (2003) no. 4, pp. 589-616. http://geodesic.mathdoc.fr/item/SM_2003_194_4_a6/

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