Semi-Symmetric Algebras: General Constructions. Part II

2000 Mathematics Subject Classification: 15A69, 15A78.

In [3] we present the construction of the semi-symmetric algebra [χ](E) of a module E over a commutative ring K with unit, which generalizes the tensor algebra T(E), the symmetric algebra S(E), and the exterior algebra ∧(E), deduce some of its functorial properties, and prove a classification theorem. In the present paper we continue the study of the semi-symmetric algebra and discuss its graded dual, the corresponding canonical bilinear form, its coalgebra structure, as well as left and right inner products. Here we present a unified treatment of these topics whose exposition in [2, A.III] is made simultaneously for the above three particular (and, without a shadow of doubt - most important) cases.