Title Algorithmic method to obtain abelian subalgebras and ideals in Lie algebras
Authors CEBALLOS GONZÁLEZ, MANUEL, Nunez, Juan , Tenorio, Angel F.
External publication Si
Scope Article
Nature Científica
JCR Quartile 3
SJR Quartile 2
JCR Impact 0.542
SJR Impact 0.412
Publication date 01/01/2012
ISI 000305484100009
DOI 10.1080/00207160.2012.688112
Abstract In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals of finite-dimensional Lie algebras, starting from the non-zero brackets in its law. In order to implement this method, we use the symbolic computation package MAPLE 12. Moreover, we also give 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 non-decomposable solvable non-nilpotent Lie algebras of dimension 6 over both the fields R and C, showing the differences between these fields.
Keywords abelian Lie subalgebra; abelian ideal; alpha invariant; beta invariant; algorithm
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