THE BIVECTOR CLIFFORD-ALGEBRA AND THE GEOMETRY OF HODGE DUAL OPERATORS

This article describes features of a natural representation of the Clifford algebra of the space of bivectors of a four-dimensional vector space, the representation space being the vector space plus its dual. Vectors and covectors are then pure spinors. The natural map taking a pure spinor to a totally null 3-bivector is shown to be intertwined with the operation of lowering or raising by a metric with the action of the Hodge dual operator. New formulae exhibiting a metric in terms of its dual operator are presented, as are a few applications.