Weight (representation theory)

In the mathematical field of representation theory, the concept of weights of an algebra A over a field F is a generalisation of that of eigenvalues. They are algebra homomorphisms from A to F, or equivalently, one-dimensional representations of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups. 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.