Symmetry classes of tensors via semigroup operands (Q1089071)

The symmetry of tensors, such as the symmetric or antisymmetric ones built on finite dimensional complex vector space may be described by a complex-valued homomorphism of symmetric group with the specification on that its action is a scalar multiplication by the value, e.g. by 1 or sign. The author states without detail developments an approach to reconstruct this condition as a universalizing operand homomorphism from the unsymmetrized tensors. He says that this approach permits a clearer and more effective treatment of these symmetries, and that freed from the multilinear setting in which they arose, it also points the way to a development of semigroup symmetries on more general universal algebras.