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Weight (representation theory) | Wikipedia audio article

This is an audio version of the Wikipedia Article: https://en.wikipedia.org/wiki/Weight_...) 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 Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago. Learning by listening is a great way to: increases imagination and understanding improves your listening skills improves your own spoken accent learn while on the move reduce eye strain Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone. Listen on Google Assistant through Extra Audio: https://assistant.google.com/services... Other Wikipedia audio articles at: https://www.youtube.com/results?searc... Upload your own Wikipedia articles through: https://github.com/nodef/wikipedia-tts Speaking Rate: 0.7940578784103096 Voice name: en-AU-Wavenet-D "I cannot teach anybody anything, I can only make them think." Socrates SUMMARY ======= 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.