Equivariant compactifications of reductive groups
Equivariant compactifications of reductive groups
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还原群的等变紧化
DOI：
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发表时间：
2002
期刊：
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通讯作者：
D. A. Timashev
中科院分区：
文献类型：
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作者：
D. A. Timashev
本文研究了约化群的等变射影紧化，这些约化群可以作为群在一个表示的射影线性算子空间中的象的闭包而得到。描述了由左/右乘法作用的群的直接平方作用的轨道的结构和相互位置，以及闭轨道邻域中紧化的局部结构。给出了紧化的正态性和平滑性的几个条件。所使用的方法是基于球面齐次空间的等变嵌入理论和约化代数半群。
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.