Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 001, 24 pages      arXiv:1301.0838      https://doi.org/10.3842/SIGMA.2014.001

On Classification of Finite-Dimensional Superbialgebras and Hopf Superalgebras

Said Aissaoui a and 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

Received February 08, 2013, in final form December 23, 2013; Published online January 02, 2014

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≤4.

Key words: superalgebra; superbialgebra; Hopf superalgebra; classification.

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