Symplectic Lie Algebras

Abstract

AbstractIn this lecture we do for the symplectic Lie algebras exactly what we did for the special linear ones in §15.1 and most of §15.2: we will first describe in general the structure of a symplectic Lie algebra (that is, give a Cartan subalgebra, find the roots, describe the Killing form, and so on). We will then work out in some detail the representations of the specific algebra \(\mathfrak{s}{{\mathfrak{p}}_{4}}\mathbb{C} \). As in the case of the corresponding analysis of the special linear Lie algebras, this is completely elementary.