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GA316
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Serre relations for Lie Superalgebras

Finite dimensional complex simple Lie algebras are classified using Cartan matrices. One of the main ingredients is Serre Relations. Lets call this Cartan-Killing theory.

I have the following questions.

Let $\mathfrak{g}$ be a basic classical simple Lie superalgebra.

Is there a similar theory for $\mathfrak g $? i.e., can $\mathfrak g$ be associated a Cartan matrix?

and

is there Serre relation in Super setting to get back the algebra from the matrix?

Kindly share your thoughts.

Thank you.

GA316
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  • 11
  • 24