CEBALLOS GONZÁLEZ, MANUEL, Nunez, Juan , Tenorio, Angel F.
Si
J. Algebra. Appl.
Article
Científica
0.373
0.588
01/06/2013
000316952300014
In this paper, we compute minimal faithful representations of filiform Lie algebras by means of strictly upper-triangular matrices. To obtain such representations, we use nilpotent Lie algebras g(n), of n x n strictly upper-triangular matrices, because any given (filiform) nilpotent Lie algebra g admits a Lie-algebra isomorphism with a subalgebra of g(n) for some n is an element of N\{1}. In this sense, we search for the lowest natural integer n such that the Lie algebra g(n) contains the filiform Lie algebra g as a subalgebra. Additionally, we give a representative of each representation.
Filiform Lie algebra; minimal faithful strictly upper-triangular matrix representation; algorithm