2009/05/29 by Valentin Vankov Iliev, Iliev, Valentin Vankov
Mathematics · #15A78 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.0905.4870
openalex publication_date 2009/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In our paper Semi-symmetric Algebras: General Constructions, J. Algebra, 148 (1992), pp. 479-496, we present the construction of the semi-symmetric algebra of a module over a commutative ring with unit, which generalizes the tensor algebra, the symmetric algebra, and the exterior algebra, 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 N. Bourbaki, Alg\` ebre, Chapitres 1--3, Hermann, Paris 1970, is made simultaneously for the above three particular (and, without a shadow of doubt - most important) cases.