@article {
author = {Arabyani, Homayoon and Khamseh, Elaheh},
title = {Pairs of Finite Dimensional Nilpotent and Filiform Lie Algebras},
journal = {Global Analysis and Discrete Mathematics},
volume = {6},
number = {2},
pages = {179-186},
year = {2021},
publisher = {Damghan University},
issn = {2476-5341},
eissn = {2476-7700},
doi = {10.22128/gadm.2021.451.1052},
abstract = {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.},
keywords = {Filiform Lie algebra,nilpotent Lie algebra,pair of Lie algebras,Schur multiplier},
url = {https://gadm.du.ac.ir/article_220.html},
eprint = {https://gadm.du.ac.ir/article_220_601f2eadba821821a3e9bde5718a002f.pdf}
}