Said Aissaoui, Abdenacer Makhlouf, “On Classification of Finite-Dimensional Superbialgebras and Hopf Superalgebras”, SIGMA, 2014, Volume 10,001, 24 pp.

On Classification of Finite-Dimensional Superbialgebras and Hopf Superalgebras

Said Aissaoui^a, Abdenacer Makhlouf^b

^a Université A-Mira, Laboratoire de Mathématiques Appliquées, Targa Ouzemmour 06000 Béjaia, Algeria
^b Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Applications, 4, rue des Frères Lumière F-68093 Mulhouse, France

Abstract: The purpose of this paper is to investigate finite-dimensional superbialgebras and Hopf superalgebras. We study connected superbialgebras and provide a classification of non-trivial superbialgebras and Hopf superalgebras in dimension $n$ with $n\leq 4$.

Keywords: superalgebra; superbialgebra; Hopf superalgebra; classification.

MSC: 16T10; 57T05; 17A70

Received: February 8, 2013; in final form December 23, 2013; Published online January 2, 2014

Language: English

DOI: 10.3842/SIGMA.2014.001