# Semi-Symmetric Algebras: General Constructions. Part II

Serdica Mathematical Journal (2010)

- Volume: 35, Issue: 1, page 39-66
- ISSN: 1310-6600

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topIliev, 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 -

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