Rendiconti del Seminario Matematico della Università di Padova

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Volume 121, 2009, pp. 121–143
DOI: 10.4171/RSMUP/121-7

Published online: 2009-06-30

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

Giovanni Gaiffi[1] and Michele Grassi[2]

(1) Università di Pisa, Italy
(2) Università di Pisa, Italy

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.

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Gaiffi Giovanni, Grassi Michele: A Geometric Realization of $sl(6, \mathbb C)$. Rend. Sem. Mat. Univ. Padova 121 (2009), 121-143. doi: 10.4171/RSMUP/121-7