PlanetMath: $\Gamma$-equivariant

(more info)

Math for the people, by the people.

Main Menu

$\Gamma$ -equivariant

(Definition)

Let $\Gamma$ be a compact Lie group acting linearly on and let be a mapping defined as $g\colon V \to V$ . Then is $\Gamma$ -equivariant if

$\displaystyle g(\gamma v)=\gamma g(v)$

for all $\gamma \in \Gamma$ , and all $v \in V$ .
Therefore if

commutes with $\Gamma$ then

is $\Gamma$ -equivariant.

Bibliography

GSS: Golubitsky, Martin. Stewart, Ian. Schaeffer, G. David.: Singularities and Groups in Bifurcation Theory (Volume II). Springer-Verlag, New York, 1988.

" $\Gamma$ -equivariant" is owned by mathcam. [ full author list (2) | owner history (1) ]

(view preamble)

Log in to rate this entry.
(view current ratings)

Cross-references: mapping, Lie group, compact

This is version 4 of $\Gamma$ -equivariant, born on 2003-08-21, modified 2007-06-24.
Object id is 4634, canonical name is GammaEquivariant.
Accessed 1517 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

None.[ View all 4 ]

Discussion

forum policy

No messages.

Interact