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Algorithm to compute abelian subalgebras and ideals in Malcev algebras
Author(s) -
Ceballos M.,
Núñez J.,
Tenorio Á. F.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3940
Subject(s) - symbolic computation , abelian group , mathematics , dimension (graph theory) , computation , maple , algebra over a field , pure mathematics , algorithm , mathematical analysis , biology , botany
In this paper, we introduce an algorithmic procedure that computes abelian subalgebras and ideals of a given finite‐dimensional Malcev algebra. All the computations are performed by using the non‐zero brackets in the law of the algebra as input. Additionally, the algorithm also computes the α and β invariants of these algebras, and as a supporting output, a list of abelian ideals and subalgebras of maximal dimension is returned too. To implement this algorithm, we have used the symbolic computation package MAPLE 12, performing a brief computational and statistical study for it and its implementation. Copyright © 2016 John Wiley & Sons, Ltd.