We prove that one can obtain natural bundles of Lie algebras on rank two s-K¨ahler manifolds, whose fibres are isomorphic respectively to so(s+1, s+1), su(s+1, s+1) and sl(2s+2,R). These bundles have natural flat connections, whose flat global sections generalize the Lefschetz operators of K¨ahler geometry and act naturally on cohomology. As a first application, we build an irreducible representation of a rational form of su(s + 1, s + 1) on (rational) Hodge classes of Abelian varieties with rational period matrix.

Lie Algebra bundles on s-Kahler manifolds, with applications to Abelian varieties

GAIFFI, GIOVANNI;GRASSI, MICHELE
2010

Abstract

We prove that one can obtain natural bundles of Lie algebras on rank two s-K¨ahler manifolds, whose fibres are isomorphic respectively to so(s+1, s+1), su(s+1, s+1) and sl(2s+2,R). These bundles have natural flat connections, whose flat global sections generalize the Lefschetz operators of K¨ahler geometry and act naturally on cohomology. As a first application, we build an irreducible representation of a rational form of su(s + 1, s + 1) on (rational) Hodge classes of Abelian varieties with rational period matrix.
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: http://hdl.handle.net/11568/205487
 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