Conjugation

A term with various uses.

The mapping $x \mapsto g^{-1} x g$ for fixed $g$ in a group; the corresponding maps in a monoid, unital ring and other algebraic structures: see Conjugate elements.

The mapping $x +iy \mapsto x - iy$ of the complex numbers, which a field automorphism of order 2, fixing the subfield of real numbers. Analogous involutory automorphisms of fields and skew fields such as the quaternions.