nLab
conjugation action

Contents

Idea

For GG a group and V 1V_1 and V 2V_2 two objects equipped with GG-action, the conjugation action on morphisms f:V 1V 2f : V_1 \to V_2 (not necessarily respecting the GG-action) is for gGg \in G

fgfg 1. f \mapsto g \circ f \circ g^{-1} \,.

The invariants of the conjugation action are the GG-action homomorphism.

Definition

For infinity-actions see at infinity-action – Conjugation action

Revised on August 28, 2013 17:48:32 by Urs Schreiber (82.113.98.24)