# $\mathrm{\Gamma}$-equivariant

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

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

for all $\gamma \in \mathrm{\Gamma}$, and all $v\in V$.

Therefore if $g$ commutes with $\mathrm{\Gamma}$ then $g$ is $\mathrm{\Gamma}$-equivariant.

[GSS]

## References

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

Title | $\mathrm{\Gamma}$-equivariant |
---|---|

Canonical name | Gammaequivariant |

Date of creation | 2013-03-22 13:53:20 |

Last modified on | 2013-03-22 13:53:20 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 7 |

Author | mathcam (2727) |

Entry type | Definition |

Classification | msc 37C80 |

Classification | msc 22-00 |