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# Difference between revisions of "Character (group theory)"

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Jitse Niesen (Talk | contribs) m (fix link to "trace") |
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− | In [[group theory]], a '''character''' may refer one of two related concepts: a [[group homomorphism]] from a group to the [[unit circle]], or the [[trace]] of a [[group representation]]. | + | In [[group theory]], a '''character''' may refer one of two related concepts: a [[group homomorphism]] from a group to the [[unit circle]], or the [[trace (mathematics)|trace]] of a [[group representation]]. |

==Group homomorphism== | ==Group homomorphism== | ||

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==Group representation== | ==Group representation== | ||

− | A ''character'' of a [[group representation]] of ''G'', which may be regarded as a homomorphism from the group ''G'' to a [[matrix]] group, is the [[trace]] of the corresponding matrix. | + | A ''character'' of a [[group representation]] of ''G'', which may be regarded as a homomorphism from the group ''G'' to a [[matrix]] group, is the [[trace (mathematics)|trace]] of the corresponding matrix. |

==See also== | ==See also== | ||

* [[Dirichlet character]] | * [[Dirichlet character]] |

## Latest revision as of 11:19, 15 June 2009

In group theory, a **character** may refer one of two related concepts: a group homomorphism from a group to the unit circle, or the trace of a group representation.

## Group homomorphism

A *character* of a group *G* is a group homomorphism from *G* to the unit circle, the multiplicative group of complex numbers of modulus one.

## Group representation

A *character* of a group representation of *G*, which may be regarded as a homomorphism from the group *G* to a matrix group, is the trace of the corresponding matrix.