A new type of gauge invariance for a collection of massless spin-2 fields

The paper develops the mathematical structure of the theories of gauge symmetries for a collection of massless spin-2 fields. The class of theories proposed do not describe any fields occuring in nature, however, it remains quite possible that similar mathematical structures may play an important role in physical theories. Some basic properties of associative commutative algebras are described, and the differential geometry of algebra-valued tensor fields on a real manifold is presented. The notion of an algebra manifold, and the differential geometry of Asup(∞) tensor fields, are both discussed. (UK)