Geodesic
Semi-Symmetric Algebras: General Constructions. Part II
Serdica Mathematical Journal, Tome 35 (2010) no. 1, pp. 39-66.

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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.
Keywords: Semi-Symmetric Power, Semi-Symmetric Algebra, Coalgebra Structure, Inner Product 
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Iliev, Valentin Vankov. Semi-Symmetric Algebras: General Constructions. Part II. Serdica Mathematical Journal, Tome 35 (2010) no. 1, pp. 39-66. http://geodesic.mathdoc.fr/item/SMJ2_2010_35_1_a2/