# $\Gamma$-equivariant

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]

## References

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