Algebras of observables of nearly canonical physical theories. II

The general problem to which this paper and earlier work [1–4] refers is discussed. The Jaeobi identity is equivalent [5] to the fulfillment of two identities corresponding to two one-dimensional irreducible inequivalent representations of the symmetric group of third order. The functional equations generated by these identities in the algebras of functions invariant with respect to the group of displacements are solved. Previously unknown examples of algebras are obtained.