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)\$

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.
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Gaiffi, Giovanni; Grassi, Michele
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11568/127722`
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