TY - JOUR
ID - 220
TI - Pairs of Finite Dimensional Nilpotent and Filiform Lie Algebras
JO - Global Analysis and Discrete Mathematics
JA - GADM
LA - en
SN - 2476-5341
AU - Arabyani, Homayoon
AU - Khamseh, Elaheh
AD - Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran.
AD - Department of Mathematics, Shahr-e-Qods Branch, Islamic Azad University Tehran,
Iran;
Y1 - 2021
PY - 2021
VL - 6
IS - 2
SP - 179
EP - 186
KW - Filiform Lie algebra
KW - nilpotent Lie algebra
KW - pair of Lie algebras
KW - Schur multiplier
DO - 10.22128/gadm.2021.451.1052
N2 - 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.
UR - https://gadm.du.ac.ir/article_220.html
L1 - https://gadm.du.ac.ir/article_220_601f2eadba821821a3e9bde5718a002f.pdf
ER -