Semi-Symmetric Algebras: General Constructions. Part II

Iliev, Valentin Vankov. "Semi-Symmetric Algebras: General Constructions. Part II." Serdica Mathematical Journal 35.1 (2010): 39-66. <http://eudml.org/doc/281402>.

@article{Iliev2010,
abstract = {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.},
author = {Iliev, Valentin Vankov},
journal = {Serdica Mathematical Journal},
keywords = {Semi-Symmetric Power; Semi-Symmetric Algebra; Coalgebra Structure; Inner Product; semi-symmetric power; semi-symmetric algebra; coalgebra structure; inner product; tensor algebra; exterior algebra; commutative ring; -ring; integral domain; free -module; canonical bilinear form},
language = {eng},
number = {1},
pages = {39-66},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Semi-Symmetric Algebras: General Constructions. Part II},
url = {http://eudml.org/doc/281402},
volume = {35},
year = {2010},
}

TY - JOUR
AU - Iliev, Valentin Vankov
TI - Semi-Symmetric Algebras: General Constructions. Part II
JO - Serdica Mathematical Journal
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 35
IS - 1
SP - 39
EP - 66
AB - 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.
LA - eng
KW - Semi-Symmetric Power; Semi-Symmetric Algebra; Coalgebra Structure; Inner Product; semi-symmetric power; semi-symmetric algebra; coalgebra structure; inner product; tensor algebra; exterior algebra; commutative ring; -ring; integral domain; free -module; canonical bilinear form
UR - http://eudml.org/doc/281402
ER -