BIQUOTIENT ACTIONS ON UNIPOTENT LIE GROUPS
2008 ◽
Vol 19
(08)
◽
pp. 997-1010
We consider pairs (V, H) of subgroups of a connected unipotent complex Lie group G for which the induced V × H-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 ℂn. Furthermore, a global slice isomorphic to ℂn 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.
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1986 ◽
Vol 40
(1)
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pp. 89-94
2007 ◽
Vol 18
(07)
◽
pp. 783-795
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2005 ◽
Vol 02
(01)
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pp. 111-125
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1994 ◽
Vol 46
(2)
◽
pp. 438-448
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2016 ◽
Vol 2016
(718)
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2011 ◽
Vol 148
(3)
◽
pp. 807-834
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