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Difference between revisions of "Conjugation"

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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 $x \mapsto g^{-1} x g$ 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 number]]s, which a field [[automorphism]] of order 2, fixing the subfield of [[real number]]s.  Analogous involutory automorphisms of fields and skew fields such as the [[quaternion]]s.
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The mapping $x +iy \mapsto x - iy$ of the [[complex number]]s, which a field [[automorphism]] of order 2, fixing the subfield of [[real number]]s.  Analogous involutory automorphisms and anti-automorphisms of fields and skew fields such as the [[quaternion]]s.

Revision as of 21:38, 29 November 2014

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=35142