Character (group theory): Difference between revisions
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imported>Richard Pinch (See also Dirichlet character) |
imported>Howard C. Berkowitz No edit summary |
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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]] of a [[group representation]]. | ||
Revision as of 19:57, 7 February 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.