Abstract:
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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