Biquotient actions on unipotent Lie groups
复变函数
2011-09-20 v1
摘要
We consider pairs (V,H) of subgroups of a connected unipotent complex Lie group G for which the induced VxH-action on G by multiplication from the left and from the right is free. We prove that this action is proper if the Lie algebra g of G is 3-step nilpotent. If g is 2-step nilpotent then there is a global slice of the action that is isomorphic to C^n. Furthermore, a global slice isomorphic to C^n exists if dim V = 1 = dim H or dim V = 1 and g is 3-step nilpotent. We give an explicit example of a 3-step nilpotent Lie group and a pair of 2-dimensional subgroups such that the induced action is proper but the corresponding geometric quotient is not affine.
引用
@article{arxiv.math/0701109,
title = {Biquotient actions on unipotent Lie groups},
author = {Annett Puettmann},
journal= {arXiv preprint arXiv:math/0701109},
year = {2011}
}