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.