JournalsrsmupVol. 121pp. 121–143

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

  • Giovanni Gaiffi

    Università di Pisa, Italy
  • Michele Grassi

    Università di Pisa, Italy
A Geometric Realization of $sl(6, \mathbb C)$ cover
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Abstract

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

Cite this article

Giovanni Gaiffi, Michele Grassi, A Geometric Realization of sl(6,C)sl(6, \mathbb C). Rend. Sem. Mat. Univ. Padova 121 (2009), pp. 121–143

DOI 10.4171/RSMUP/121-7