Mixing of all orders of Lie groups actions

Abstract

Professor Stepin has pointed out that in order for the proof of Theorem 1 to work one needs to add to the assumptions of the theorem the requirement that the center of G is finite.This additional change is required to exclude cases where the group G has a nontrivial connected compact central subgroup.In such a case the argument doesn't work as the action of the unipotent element we produce may be non-ergodic.When G has a finite center and is Ad-proper we can choose the open ball f~ (see page 238 line -9) so that the element (h~+ 1, h~+2 .... , hk) has a nontrivial unipotent image under the adjoint representation and hence generates an unbounded subgroup and acts ergodically.

Locations

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