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It is often claimed [PST1] that the (Hodge type) duality operation is definedonly in even dimensional spacetimes and that self-duality is further restrictedto twice-odd dimensional spacetime theories.  The purpose of this paper is to extend the notion of both duality symmetry aswell as self-duality.  By considering tensorial doublets, we introduce a novel well-defined notionof self-duality based on a duality Hodge-type operation in arbitrary dimensionand for any rank of these tensors. Thus, a generalized Self-Dual Action isdefined such that equations of motion are the claimed generalized self-dualityrelations. We observe in addition, that taking the proper limit on theparameters of this action, it always provides us with a master-action, whichinterpolates models well-studied in physics; by considering a particular limit,we find an action which describes an interesting type of relation, referred toas semi-self-duality, which results to be the parent action between Maxwell-type actions.  Finally, we apply these ideas to construct manifest Hodge-type self-dualsolutions in a (2+1)-dimensional version of the Maxwell's theory.

Hodge-type self(antiself)-duality for general p-form fields in arbitrary dimensions