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Results tagged with lie-algebras
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user 117247
Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds.
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Physicists misuse the term "Kac Moody algebra". Does that bring problems?
In physics textbooks one frequently sees the name (affine) Kac Moody algebra used to describe the universal (one dimensional) central extension of the loop algebra of a semisimple algebra. But this is …
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Monoidal category of irreducible highest weight modules of the Virasoro algebra
I'm trying to see if I can construct a monoidal category $\mathbf{C}$ whose objects are the irreducible unitary highest weight representations of the Virasoro algebra.
I am thinking on doing the fol …
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GKO construction for (Super-)Virasoro algebras
I am reading the paper "Unitary Representations of the Virasoro and Super-Virasoro Algebras" by Goddard, Kent, Olive. In many places, the authors claim results without any justification, or with obscu …
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The use of Schur's lemma for Lie algebras in physics (CFT)
Anytime a one-dimensional central extension appears in the physics literature, immediately they assume that in any irreducible representation the central charge will be a multiple of the identity, imp …
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GKO (or coset) construction - all possible highest weights $h$
I am reading the famous paper "Unitary Representations of the Virasoro and Super-Virasoro Algebras" by Goddard, Kent, Olive.
From a compact simple Lie algebra $\mathfrak{g}$ and a Lie subalgebra $\ma …
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Different views on Highest weight irreducible modules of the Virasoro algebra
Every highest weight irreducible representation of the Virasoro algebra can be labelled uniquely by a pair $(c,h)$ of complex numbers [1]. This module can be written as quotient of the unique (up to i …
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