Weight (representation Theory)
In the mathematical field of representation theory, a weight of an algebra A over a field F is an algebra homomorphism from A to F – a linear functional – or equivalently, a one dimensional representation 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.
Read more about Weight (representation Theory): Semisimple Lie Algebras
Famous quotes containing the word weight:
“Prose on certain occasions can bear a great deal of poetry; on the other hand, poetry sinks and swoons under a moderate weight of prose.”
—Walter Savage Landor (17751864)