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arXiv · 1109.0894

Generalized duality for k-forms

Frank Klinker
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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 $Ω$. 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 $Ω$ is invariant with respect to a subalgebra of $\mathfrak{so}(V)$. Furthermore, we give examples for the invariant case as well as for the case of discrete symmetry.

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Frank Klinker. 2011-09-05. Generalized duality for k-forms. https://doi.org/10.1016/j.geomphys.2011.07.007

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