Editing Weight (representation theory) (section)

{{Short description|Concept in Lie algebra representation theory}}
In the [[mathematics|mathematical]] field of [[representation theory]], a '''weight''' of an [[algebra over a field|algebra]] ''A'' over a [[field (mathematics)|field]] '''F''' is an [[algebra homomorphism]] from ''A'' to '''F''', or equivalently, a one-dimensional [[algebra representation|representation]] of ''A'' over '''F'''. It is the algebra analogue of a [[multiplicative character]] of a [[group (mathematics)|group]]. The importance of the concept, however, stems from its application to [[Lie algebra representation|representations of Lie algebras]] and hence also to [[group representation|representations]] of [[Algebraic group|algebraic]] and [[Lie group]]s. In this context, a '''weight of a representation''' is a generalization of the notion of an [[eigenvalue]], and the corresponding [[eigenspace]] is called a '''weight space'''.