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:
“In a town-meeting, the great secret of political science was uncovered, and the problem solved, how to give every individual his fair weight in the government, without any disorder from numbers. In a town-meeting, the roots of society were reached. Here the rich gave counsel, but the poor also; and moreover, the just and the unjust.”
—Ralph Waldo Emerson (1803–1882)