Weight (representation theory) | Wikipedia audio article
Channel: wikipedia tts
Date: 29/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Weight_(representation_theory)


00:00:38 1 Motivation and general concept
00:04:13 2 Weights in the representation theory of semisimple Lie algebras
00:04:29 2.1 Weight of a representation
00:05:31 2.2 Action of the root vectors
00:08:44 2.3 Integral element
00:12:07 2.4 Partial ordering on the space of weights
00:21:47 2.5 Dominant weight
00:24:27 2.6 Theorem of the highest weight
00:25:38 2.7 Highest-weight module
00:27:07 3 See also
00:28:47 4 Notes



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SUMMARY
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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.