Generalized duality for k-forms

Abstract

We give the definition of a duality that is applicable to arbitrary k-forms. The operator that defines the duality depends on a fixed form omega. Our definition extends in a very natural way the Hodge duality of n-forms in 2n dimensional spaces and the generalized duality of two-forms. We discuss the properties of the duality in the case where omega is invariant with respect to a subalgebra of so(V). Furthermore, we give examples for the invariant case as well as for the case of discrete symmetry.