Niroomand, Peyman; Johari, Farangis; Parvizi, Mohsen Capable Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field. (English) Zbl 1472.17045 Linear Multilinear Algebra 67, No. 3, 542-554 (2019). Summary: In this paper, we classify all capable nilpotent Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field. Moreover, the explicit structure of such Lie algebras of class 3 is given. Cited in 12 Documents MSC: 17B30 Solvable, nilpotent (super)algebras 17B05 Structure theory for Lie algebras and superalgebras 17B99 Lie algebras and Lie superalgebras Keywords:capability; Schur multiplier; generalized Heisenberg Lie algebras; stem Lie algebras PDFBibTeX XMLCite \textit{P. Niroomand} et al., Linear Multilinear Algebra 67, No. 3, 542--554 (2019; Zbl 1472.17045) Full Text: DOI arXiv References: [1] Hall, P., The classification of prime power groups, J Reine Angew Math, 182, 130-141 (1940) · JFM 66.0081.01 [2] Beyl, Fr; Felgner, U.; Schmid, P., On groups occurring as center factor groups, J Algebra, 61, 161-177 (1970) · Zbl 0428.20028 [3] Heineken, H., Nilpotent groups of class 2 that can appear as central quotient groups, Rend Sem Mat Univ Padova, 84, 241-248 (1990) · Zbl 0722.20011 [4] Salemkar, Ar; Alamian, V.; Mohammadzadeh, H., Some properties of the Schur multiplier and covers of Lie Algebras, Commun Algebra, 36, 697-707 (2008) · Zbl 1132.17003 [5] Ellis, G., A non-abelian tensor product of Lie algebras, Glasg Math J, 39, 101-120 (1991) · Zbl 0724.17016 [6] Niroomand, P.; Parvizi, M.; Russo, Fg, Some criteria for detecting capable Lie algebras, J Algebra, 384, 36-44 (2013) · Zbl 1318.17003 [7] Niroomand, P.; Johari, F.; Parvizi, M., On the capability and Schur multiplier of nilpotent Lie algebra of class two, Proc Amer Math Soc, 144, 4157-4168 (2016) · Zbl 1383.17007 [8] Batten, P.; Moneyhun, K.; Stitzinger, E., On characterizing nilpotent Lie algebras by their multipliers, Commun Algebra, 24, 4319-4330 (1996) · Zbl 0893.17008 [9] Batten, P.; Stitzinger, E., On covers of Lie algebras, Commun Algebra, 24, 4301-4317 (1996) · Zbl 0893.17004 [10] Bosko, L., On Schur multiplier of Lie algebras and groups of maximal class, Internat J Algebra Comput, 20, 807-821 (2010) · Zbl 1223.17015 [11] Hardy, P.; Stitzinger, E., On characterizing nilpotent Lie algebras by their multipliers t(L) = 3; 4; 5; 6, Commun Algebra, 26, 11, 3527-3539 (1998) · Zbl 0916.17008 [12] Moneyhun, K., Isoclinisms in Lie algebras, Algebras Groups Geom, 11, 9-22 (1994) · Zbl 0801.17005 [13] Niroomand, P.; Russo, Fg, A note on the Schur multiplier of a nilpotent Lie algebra, Commun Algebra, 39, 1293-1297 (2011) · Zbl 1250.17019 [14] Niroomand, P.; Russo, Fg, A restriction on the Schur multiplier of nilpotent Lie algebras, Electron J Linear Algebra, 22, 1-9 (2011) · Zbl 1277.17007 [15] Niroomand, P., On the dimension of the Schur multiplier of nilpotent Lie algebras, Cent Eur J Math, 9, 57-64 (2011) · Zbl 1281.17015 [16] Johari, F.; Parvizi, M.; Niroomand, P., Capability and Schur multiplier of a pair of Lie algebras, J Geom Phys, 114, 184-196 (2017) · Zbl 1380.17012 [17] Cicalò, S.; De Graaf, Wa; Schneider, C., Six-dimensional nilpotent Lie algebras, Linear Algebra Appl, 436, 1, 163-189 (2012) · Zbl 1250.17017 [18] Gong, Mp, Classification of nilpotent Lie algebras of dimension 7 (over algebraically closed fields and R) [a thesis in Waterloo], Ontario, Canada (1998) [19] De Graaf, Wa, Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2, Algebra, 309, 640-653 (2007) · Zbl 1137.17012 [20] Zack, Lm, Nilpotent Lie algebras with a small second derived quotient, Commun Algebra, 36, 4607-4619 (2008) · Zbl 1178.17010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.