English

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}
}