Kaplansky's Construction Type and Classification of Weak bialgebras and Weak Hopf algebras
Rings and Algebras
2010-01-14 v1 Quantum Algebra
Abstract
In this paper, we study weak bialgebras and weak Hopf algebras. These algebras form a class wider than bialgebras respectively Hopf algebras. The main results of this paper are Kaplansky's constructions type which lead to weak bialgebras or weak Hopf algebras starting from a regular algebra or a bialgebra. Also we provide a classification of 2-dimensional and 3-dimensional weak bialgebras and weak Hopf algebras. We determine then the stabilizer group and the representative of these classes, the action being that of the linear group.
Keywords
Cite
@article{arxiv.1001.2194,
title = {Kaplansky's Construction Type and Classification of Weak bialgebras and Weak Hopf algebras},
author = {Zoheir Chebel and Abdenacer Makhlouf},
journal= {arXiv preprint arXiv:1001.2194},
year = {2010}
}