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On the conjugacy and isomorphism problems for stabilizers of Lie group actions

Published online by Cambridge University Press:  02 April 2001

VALENTIN YA. GOLODETS  and
SERGEY D. SINEL'SHCHIKOV
VALENTIN YA. GOLODETS
Affiliation:
B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Kharkov, Ukraine (e-mail: [email protected], [email protected])
SERGEY D. SINEL'SHCHIKOV
Affiliation:
B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, Kharkov, Ukraine (e-mail: [email protected], [email protected])
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Abstract

The spaces of subgroups and Lie subalgebras with the group actions by conjugations are considered for real Lie groups. Our approach allows one to apply the properties of algebraically regular transformation groups to finding the conditions when those actions turn out to be type I. It follows, in particular, that in this case the stability groups for all the ergodic actions of such groups are conjugate (for example when the stability groups are compact). The isomorphism of the stability groups for ergodic actions is also established under some assumptions. A number of examples of non-conjugate and non-isomorphic stability groups are presented.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 2 , April 1999 , pp. 391 - 411
Copyright
1999 Cambridge University Press

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