Summary: Given an orientable weakly self-dual manifold $X$ of rank two (see the second author, Asian J. Math. 9, No. 1, 79--101 (2005; Zbl 1085.14035)), we build a geometric realization of the Lie algebra $\germ{sl}(6,\Bbb C)$ as a naturally defined algebra $L$ of endomorphisms of the space of differential forms of $X$. We provide an explicit description of Serre generators in terms of natural generators of $L$. 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.
A geometric realization of $mathbf{sl}(6,C)$
GRASSI, MICHELE
2009-01-01
Abstract
Summary: Given an orientable weakly self-dual manifold $X$ of rank two (see the second author, Asian J. Math. 9, No. 1, 79--101 (2005; Zbl 1085.14035)), we build a geometric realization of the Lie algebra $\germ{sl}(6,\Bbb C)$ as a naturally defined algebra $L$ of endomorphisms of the space of differential forms of $X$. We provide an explicit description of Serre generators in terms of natural generators of $L$. 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.File in questo prodotto:
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