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Weight (representation theory): Mathematics, Representation Theory, Algebra Over a Field, Theta Function, Pendulum, Trigonometry, Weierstrass's Elliptic Functions, Quarter Period, Complex Plane - Couverture souple

 
9786130364199: Weight (representation theory): Mathematics, Representation Theory, Algebra Over a Field, Theta Function, Pendulum, Trigonometry, Weierstrass's Elliptic Functions, Quarter Period, Complex Plane

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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, 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.

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