Lie Group Actions on a Cayley Projective Plane and a Note on Homogeneous Spaces of Prime Euler Characteristic

1976 ◽  
Vol 98 (3) ◽  
pp. 655 ◽  
Author(s):  
Theodore Chang ◽  
Tor Skjelbred
Keyword(s):  
Projective Plane ◽  
Euler Characteristic ◽  
Lie Group ◽  
Homogeneous Spaces ◽  
Group Actions ◽  
Lie Group Actions

scholarly journals Higher-order orbifold Euler characteristics for compact Lie group actions

2015 ◽  
Vol 145 (6) ◽  
pp. 1215-1222 ◽  
Author(s):  
S. M. Gusein-Zade ◽  
I. Luengo ◽  
A. Melle-Hernández
Keyword(s):  
Euler Characteristic ◽  
Lie Group ◽  
Group Actions ◽  
Wreath Products ◽  
Higher Order ◽  
Compact Lie Group ◽  
Euler Characteristics ◽  
Finite Group Actions ◽  
Lie Group Actions ◽  
Generating Series

We generalize the notions of the orbifold Euler characteristic and of the higher-order orbifold Euler characteristics to spaces with actions of a compact Lie group using integration with respect to the Euler characteristic instead of the summation over finite sets. We show that the equation for the generating series of the kth-order orbifold Euler characteristics of the Cartesian products of the space with the wreath products actions proved by Tamanoi for finite group actions and by Farsi and Seaton for compact Lie group actions with finite isotropy subgroups holds in this case as well.

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

1999 ◽  
Vol 19 (2) ◽  
pp. 391-411 ◽  
Author(s):  
VALENTIN YA. GOLODETS ◽  
SERGEY D. SINEL'SHCHIKOV
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Group Actions ◽  
Transformation Groups ◽  
Type I ◽  
Lie Group Actions ◽  
The Stability ◽  
Regular Transformation

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.

scholarly journals Equivariant K -theory of compact Lie group actions with maximal rank isotropy

2012 ◽  
Vol 5 (2) ◽  
pp. 431-457 ◽  
Author(s):  
Alejandro Adem ◽  
José Manuel Gómez
Keyword(s):  
Lie Group ◽  
Group Actions ◽  
Maximal Rank ◽  
Compact Lie Group ◽  
Lie Group Actions ◽  
K Theory

scholarly journals Quantizations of compact Lie group actions

2014 ◽  
Vol 80 ◽  
pp. 26-36
Author(s):  
Hilja L. Huru ◽  
Valentin V. Lychagin
Keyword(s):  
Lie Group ◽  
Group Actions ◽  
Compact Lie Group ◽  
Lie Group Actions
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