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.
Gaiffi, Giovanni; Grassi, Michele
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/127722
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact