The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of investigation was initiated for the space of elasticity tensors. Since then, different authors solved this problem for other kinds of physics such as photoelectricity, ...

We consider generators of algebraic curvature tensors R which can be constructed by a Young symmetrization of product tensors U ⊗ w or w ⊗ U , where U and w are covariant tensors of order 3 and 1. We assume that U belongs to a class of the infinite set S of irreducible symmetry classes characterized by the partition (2 1). We show that the set S contains exactly one symmetry class S0 ∈ S whose ...