|
|
|
|
 -equivariant
|
(Definition)
|
|
|
Let $\Gamma$ be a compact Lie group acting linearly on $V$ and let $g$ be a mapping defined as $g\colon V \to V$ Then $g$ is $\Gamma$ equivariant if $$g(\gamma v)=\gamma g(v)$$ for all $\gamma \in \Gamma$ and all $v \in V$
Therefore if $g$ commutes with $\Gamma$ then $g$ is $\Gamma$ equivariant.
[GSS]
- GSS
- Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David.: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.
|
" -equivariant" is owned by mathcam. [ full author list (2) | owner history (1) ]
|
|
(view preamble | get metadata)
Cross-references: mapping, Lie group, compact
This is version 4 of  -equivariant, born on 2003-08-21, modified 2007-06-24.
Object id is 4634, canonical name is GammaEquivariant.
Accessed 1917 times total.
Classification:
| AMS MSC: | 37C80 (Dynamical systems and ergodic theory :: Smooth dynamical systems: general theory :: Symmetries, equivariant dynamical systems) | | | 22-00 (Topological groups, Lie groups :: General reference works ) |
|
|
|
|
|
|
Pending Errata and Addenda
|
|
|
|
|
|
|
|
|
|
|
