The Schur multiplier of a pair of groups was introduced by Ellis in 1998. In this paper, we study the Schur multiplier and the c-nilpotent multiplier of pairs of Lie algebras and give some conditions under which the Schur multiplier of a pair of Lie algebras is trivial. Moreover, we give some conditions under which the higher multiplier of a pair of Lie algebras is not trivial.
H. Arabyani, Bounds for the dimension of the c-nilpotent multiplier of a pair of Lie algebras, Bull. Iranian Math. Soc., 43, 2411–2418 (2017).
H. Arabyani, Some results on the c-nilpotent multiplier of a pair of Lie algebras, Bull.Iranian Math. Soc., 45, 205–212 (2019).
H. Arabyani, Some Results on the Higher Multiplier of a Pair of Groups, Southeast Asian Bull. Math. 45, 429–435 (2021).
H. Arabyani, F. Saeedi, M. R. R. Moghaddam, E. Khamseh, Characterization of nilpotent Lie algebras pair by their Schur multipliers, Comm. Algebra, 42, 5474–5483 (2014).
H. Arabyani, H. Safa, Some properties of c-covers of a pair of Lie algebras, Quaest. Math., 42, 37–45 (2019).
M. Araskhan, On the c-covers and a special ideal of Lie algebras, Iran. J. Sci. Technol. Trans. A. Sci., 40, 165–169 (2016).
L. Bosko, E. Stitzinger, Schur multipliers of nilpotent Lie algebras, arXiv:1103. 1812v1 [math. RA] 9 Mar 2011.
B. Edalatzadeh, S. N. Hosseini, A. R. Salemkar, On characterizing pairs of nilpotent Lie algebras by their second relative homologies, J. Algebra, 549, 112–127 (2020).
A. Gholami, Z. Mohammad Abadi, S. Heidarian, Some generalized varietal properties on pair of groups, Southeast Asian Bull. Math., 36, 301–308 (2012).
A. Hokmabadi, A. Pourmirzaei, S. Kayvanfar, A criterion for c-capability of pairs of groups, Tbilisi Mathematical Journal, 5, 31–38 (2012).
K. Moneyhun, Isoclinisms in Lie algebras, Algebras Groups Geom., 11, 9–22 (1994).
P. Niroomand, F. Johari, The structure, capability and the Schur multiplier of generalized Heisenberg Lie algebras, J. Algebra, 505, 482–489 (2018).
P. Niroomand, F. Johari, M. Parvizi, Capable Lie algebras with the derived subalgebra of dimension 2 over an arbitrary field, Linear Multilinear Algebra, 67, 542–554 (2019).
M. R. Rismanchian, M. Molavi, M. Araskhan, On dimension and homological methods of the (higher) Schur multiplier of a pair of Lie algebras, Comm. Algebra, 45, 4707–4716 (2017).
Z. Riyahi, A. R. Salemkar, A remark on the Schur multiplier of nilpotent Lie algebras, J. Algebra, 438, 1–6 (2015).
F. Saeedi, A. R. Salemkar, B. Edalatzadeh, The commutator subalgebra and Schur multiplier of a pair of nilpotent Lie algebras, J. Lie Theory, 21, 491–498 (2011).
H. Safa, H. Arabyani, On c-nilpotent multiplier and c-covers of a pair of Lie algebras, Comm. Algebra., 45, 4429-4434 (2017).
H. Safa, H. Arabyani, Capable pairs of Lie algebras, Math. Proc. R. Ir. Acad., 118, 39–45 (2018).
A. R. Salemkar, B. Edalatzadeh, M. Araskhan, Some inequalities for the dimension of the c-nilpotent multiplier of Lie algebras, J. Algebra, 322, 1575–1585 (2009).
Arabyani, H. (2021). The Schur Multiplier of Pairs of Nilpotent Lie Algebras. Analytical and Numerical Solutions for Nonlinear Equations, 6(2), 215-220. doi: 10.22128/gadm.2021.457.1053
MLA
Homayoon Arabyani. "The Schur Multiplier of Pairs of Nilpotent Lie Algebras", Analytical and Numerical Solutions for Nonlinear Equations, 6, 2, 2021, 215-220. doi: 10.22128/gadm.2021.457.1053
HARVARD
Arabyani, H. (2021). 'The Schur Multiplier of Pairs of Nilpotent Lie Algebras', Analytical and Numerical Solutions for Nonlinear Equations, 6(2), pp. 215-220. doi: 10.22128/gadm.2021.457.1053
VANCOUVER
Arabyani, H. The Schur Multiplier of Pairs of Nilpotent Lie Algebras. Analytical and Numerical Solutions for Nonlinear Equations, 2021; 6(2): 215-220. doi: 10.22128/gadm.2021.457.1053
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