Kac-Moody algebras and Lie algebras of regular vector fields on tori

M. Rausch de Traubenberg, M. J. Slupinski

We consider the problem of representing the Kac-Moody algebra $\mathfrak{g}(N)$ specified by an $r\times r$ indecomposable generalised Cartan matrix $N$ as vector fields on the tor…