A Geometric Realization of $sl(6, \mathbb C)$

Abstract

Given an orientable weakly self-dual manifold X of rank two, webuild a geometric realization of the Lie algebra sl(6,C) as a naturally definedalgebra LC of endomorphisms of the space of differential forms ofX. We provide an explicit description of Serre generators interms of natural generators of LC. This construction gives abundle on X which is related to the search for a natural Gaugetheory on X. We consider this paper as a first step in the study of a rich and interesting algebraic structure.