Properties of an Associative Algebra of Tensor Fields. Duality and Dirac Identities

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Abstract
An algebra of forms in Minkowski space has been constructed. A multiplication between forms is defined as an extension of the quaternionic multiplications. The algebra obtained is associative with respect to this multiplication of order 16. Duality is expressed as (new) multiplication by a basis element. Vector identities in the algebra lead to a number of new trace identities. A new derivative operator expresses the four Maxwell equations in an especially transparent form.

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