Classification of types A and A_+ from low dimensional standard and non-standard filiform Lie Algebras

Kurniadi, Edi
Parmikanti, Kankan
Badrulfalah, Badrulfalah

Journal of Natural Sciences and Mathematics Research
Vol. 9 No. 2 (2023): December

In this paper, we study low-dimensional Filiform Lie algebras. Specifically, three-dimensional standard Filiform Lie algebras and five-dimensional non-standard Filiform Lie algebras. The classification method was given in the following stage. For given a low-dimensional Filiform Lie algebra, we compute its second centre. We showed that three-dimensional Filiform Lie algebra-called Heisenberg Lie algebra-is type ???? and ????+ as well. On the other hand, for ????≥3, the standard Filiform Lie algebras are type ???? but not type ????+. In this case, we give a concrete example of case five-dimensional Heisenberg Lie algebra. Moreover, we proved that five-dimensional non-standard Filiform Lie algebra is type ???? but not type ????+. It is still an open problem to classify types ???? and ????+ for the general case of non-standard Filiform Lie algebra of dimension ≥6.