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 and anti-automorphisms of fields and skew fields such as the [[quaternion]]s. | + | 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 [[involution|involutory]] automorphisms and anti-automorphisms of fields and skew fields such as the [[quaternion]]s. |
Latest 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=35145
Conjugation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conjugation&oldid=35145