MHB Question about the "E" Lie algebras

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E_6 is primarily defined by its Dynkin diagram, which serves as a graphical representation of its root system and structure. The Dynkin diagram provides essential information about the algebra's properties and relationships. While the diagram is significant, E_6 can also be characterized through its generators and relations in the context of Lie algebras. Understanding the connections between the Dynkin diagram and the algebra's definition is crucial for studying E_6. Further exploration of the text may reveal more detailed definitions and properties of E_6.
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I'm in chapter 2 of my Lie algebra text. I have an interest in E_8 but I'm only going to work my way up to E_6 as it has fewer operators. Anyway for now I only have a quick question: Is E_6 defined by its Dynkin diagram or is E_6 defined by something else and the Dynkin diagram follows from that? I haven't been able to find a definition of what E_6 is in my text yet.

-Dan
 

Thread 'Confusion about the Moyal-Weyl twist'

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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