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

作者：Ceballos Manuel^*; Nunez Juan; Tenorio Angel F

来源：International Journal of Computer Mathematics, 2015, 92(9): 1838-1854.

DOI：10.1080/00207160.2014.884216

• beta invariant
• Leibniz algebra
• abelian ideal
• algorithm
• abelian subalgebra
• alpha invariant
• 68Q25
• 17A60
• 17-08
• 17A32
• 68W30

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 .

• 出版日期2015-9-2