%0 Journal Article
%T Pairs of Finite Dimensional Nilpotent and Filiform Lie Algebras
%J Global Analysis and Discrete Mathematics
%I Damghan University
%Z 2476-5341
%A Arabyani, Homayoon
%A Khamseh, Elaheh
%D 2021
%\ 11/01/2021
%V 6
%N 2
%P 179-186
%! Pairs of Finite Dimensional Nilpotent and Filiform Lie Algebras
%K Filiform Lie algebra
%K nilpotent Lie algebra
%K pair of Lie algebras
%K Schur multiplier
%R 10.22128/gadm.2021.451.1052
%X Let (N,L) be a pair of finite dimensional nilpotent Lie algebras. If N admits a complement K in L such that dim N = n and dim K = m, then dim M(N,L) = 1/2n(n + 2m - 1) - t(N,L), where M(N,L) is the Schur multiplier of the pair (N,L) and t(N,L) is a non-negative integer. In this paper, we characterize the pair (N,L) for t(N,L)=0, 1, 2, … , 23, where N is a finite dimensional filiform Lie algebra and N,K are ideals of L such that L = N ⊕ K. Moreover, we classify the pair (N,L) for s′ (N,L) = 3, where S′ (N,L) = 1/2 (n - 1)(n - 2) + 1 + (n - 1)m – dim M(N,L), L is a finite dimensional nilpotent Lie algebra and N is a non-abelian ideal of L.
%U https://gadm.du.ac.ir/article_220_601f2eadba821821a3e9bde5718a002f.pdf