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.
Z. Chebel. A. Makhlouf. "Kaplansky's Type Constructions for Weak Bialgebras and Weak Hopf Algebras." J. Gen. Lie Theory Appl. 9 (S1) 1 - 9, 2015. https://doi.org/10.4172/1736-4337.S1-008