Character (group theory): Difference between revisions
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imported>Howard C. Berkowitz No edit summary |
imported>Jitse Niesen 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]] | ||
Revision as of 06:19, 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.