Journal de théorie et applications du mensonge généralisé

Kaplansky's Type Constructions for Weak Bialgebras and Weak Hopf Algebras

Abstract

Chebel Z and Makhlouf A

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 type constructions 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.