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Affine Lie algebra and Algebraic character

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Affine Lie algebra and Algebraic character

Affine Lie algebra vs. Algebraic character

In mathematics, an affine Lie algebra is an infinite-dimensional Lie algebra that is constructed in a canonical fashion out of a finite-dimensional simple Lie algebra. Algebraic character is a formal expression attached to a module in representation theory of semisimple Lie algebras that generalizes the character of a finite-dimensional representation and is analogous to the Harish-Chandra character of the representations of semisimple Lie groups.

Similarities between Affine Lie algebra and Algebraic character

Affine Lie algebra and Algebraic character have 6 things in common (in Unionpedia): Kac–Moody algebra, Representation theory, Semisimple Lie algebra, Verma module, Weight (representation theory), Weyl character formula.

Kac–Moody algebra

In mathematics, a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently discovered them) is a Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix.

Affine Lie algebra and Kac–Moody algebra · Algebraic character and Kac–Moody algebra · See more »

Representation theory

Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.

Affine Lie algebra and Representation theory · Algebraic character and Representation theory · See more »

Semisimple Lie algebra

In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e., non-abelian Lie algebras \mathfrak g whose only ideals are and \mathfrak g itself.

Affine Lie algebra and Semisimple Lie algebra · Algebraic character and Semisimple Lie algebra · See more »

Verma module

Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics.

Affine Lie algebra and Verma module · Algebraic character and Verma module · See more »

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, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue of a multiplicative character of a group.

Affine Lie algebra and Weight (representation theory) · Algebraic character and Weight (representation theory) · See more »

Weyl character formula

In mathematics, the Weyl character formula in representation theory describes the characters of irreducible representations of compact Lie groups in terms of their highest weights.

Affine Lie algebra and Weyl character formula · Algebraic character and Weyl character formula · See more »

The list above answers the following questions

Affine Lie algebra and Algebraic character Comparison

Affine Lie algebra has 39 relations, while Algebraic character has 9. As they have in common 6, the Jaccard index is 12.50% = 6 / (39 + 9).

References

This article shows the relationship between Affine Lie algebra and Algebraic character. To access each article from which the information was extracted, please visit:

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