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Difference between revisions of "Character (group theory)"

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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]].
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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 (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.
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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]]

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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.

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.

See also