Questions tagged [kac-moody-algebras]

For questions regarding the definition, properties and types of the Kac-Moody algebras.

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Structure of affine Lie algebras

It is well-known that to every simple Lie algebra $\mathfrak{g}$ one can associate an affine Kac-Moody algebra by a double extension (once by a 2-cocycle and once by a derivation). One can then show ...
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Definition of the $O$ category for Kac Moody algebras

In Carter's book "Lie algebras of finite and affine type", he defines the $O$ category for Kac Moody algebras as follows: I do not understand in what sense $\lambda<\lambda_i$ on the last part of ...
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Selection rules for Kazama Suzuki models

I am following a paper in mathematical physics by Nozaki: "Comments on D-branes in Kazama-Suzuki models and Landau-Ginzburg theories". I find it a bit vague and have a couple of specific questions. ...
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Clarification on Kac Moody algebras and the different meanings in mathematics and physics

I am confused by the way that mathematicians and physicists use the words "Kac Moody algebra", and "loop algebra", and how exactly these concepts relate to one another. I will write down what I ...
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What is the matrix of the monster Lie algebra?

In Richard Borcherds' proof of monstrous moonshine, he constructs a "monster Lie algebra", which is a $\mathbb Z^2$-graded, infinite-dimensional Lie algebra with a contravariant bilinear form acted on ...
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About the definition of Kac-Moody algebras

I'm following Kac's book on Infinite dimensional Lie algebras and I have just seen the definition of a Kac-Moody algebra associated with a generalized Cartan matrix $A$. Prior in the text, it was ...
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The elements $f_1,\cdots, f_n$ generate $\mathfrak{\tilde n_{-} }$ freely

I've started studying Kac-Moody algebras and free lie algebras is a really new thing for me. I am trying to understand the statement (b) of theorem 1.2 in the following book Theorem 1.2, statement (b)...