Algorithmic procedure to compute abelian subalgebras and ideals of maximal dimension of Leibniz algebras

Abstract

In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals of a given finite-dimensional Leibniz algebra, starting from the non-zero brackets in its law. In order to implement this method, the symbolic computation package MAPLE 12 is used. Moreover, we also show a brief computational study considering both the computing time and the memory used in the two main routines of the implementation. Finally, we determine the maximal dimension of abelian subalgebras and ideals for 3-dimensional Leibniz algebras and 4-dimensional solvable ones over $\mathbb{C}$.

Keywords:

• Leibniz algebra
• abelian subalgebra
• abelian ideal
• α invariant
• β invariant
• algorithm

2010 AMS Subject Classifications:

• 17A32
• 17A60
• 17–08
• 68W30
• 68Q25