MHB Deriving Structure Factors for Lie Algebras | Dan's Project

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Dan is nearing completion of a project focused on deriving structure factors from Dynkin diagrams of Lie algebras. He expresses confidence in his findings but seeks verification for accuracy. Dan requests resources or lists of structure factors specifically for Lie algebras labeled a, b, c, and d. The discussion highlights the importance of cross-checking results in mathematical research. Access to reliable references would enhance the validity of his work.
topsquark
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I am in the final stages of the project I've been working on: Taking a Dynkin diagram and deriving the structure factors for the Lie algebra it represents. Yay me!

However. I am confident in my work but it would still be really nice to be able to check them. Does anyone know where to find a list of structure factors for the Lie algebras a, b, c, and d?

Thanks!

-Dan
 
I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...

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