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Weight (representation theory)

In the mathematical field of representation theory, the concept of weights of an algebra A over a field F is a generalisation of that of eigenvalues. They are algebra homomorphisms from A to F, or equivalently, one-dimensional representations of A over F. It is the algebra analogue of a multiplicative character of a group. The importance of the concept…

Motivation and general concept, Weights in the representation theory of semisimple Lie algebras & Overview

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Motivation and general concept

MatricesDiagonalizableCommuteSimultaneously diagonalizeSemisimple
23 related topics

Weights in the representation theory of semisimple Lie algebras

Semisimple Lie algebraCartan subalgebraEigenbasisAdjoint representationPositive roots
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Overview

MathematicalRepresentation theoryAlgebraFieldEigenvalue
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Weights in the representation theory of semisimple Lie algebras

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Weight (representation theory)

Nodes59
Edges58
Triples0
Avg. degree1.97
Density0.033898
Components1

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displaystyle mathfrak weight algebra lambda representation lie weights roots space group integral root element representations finite-dimensional elements linear alpha notion

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