# Conjugation

From Encyclopedia of Mathematics

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 and anti-automorphisms of fields and skew fields such as the quaternions.

**How to Cite This Entry:**

Conjugation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Conjugation&oldid=35145