Algorithm for Testing the Leibniz Algebra Structure

Abstract. Given a basis of a vector space V over a field K and a multiplication table which defines a bilinear map on V , we develop a computer program on Mathematica which checks if the bilinear map satisfies the Leibniz identity, that is, if the multiplication table endows V with a Leibniz algebra structure. In case of a positive answer, the program informs whether the structure corresponds to a Lie algebra or not, that is, if the bilinear map is skew-symmetric or not. The algorithm is based on the computation of a Gr

• Type: Journal
• Year: 2009
• Where: EUROCAST
• Authors: José Manuel Casas, Manuel A. Insua, Manuel Ladra, Susana Ladra
• Keywords: Algebras, Bilinear Map, EUROCAST 2009, Hardware, Leibniz Algebra