Abstract
The Schur multiplier of a Lie algebra L, was introduced by Batten et al. (Commun Algebra 24:4319–4330, 1996). Salemkar and colleagues generalized the concept of the Schur multiplier to the c-nilpotent multiplier. Recently, the author introduced some exact sequences and gived some upper bounds for the dimension of the c-nilpotent multiplier of a pair of Lie algebras. In the present paper, we will extend these results. Moreover, we give some isomorphisms for the c-nilpotent multiplier of a pair of Lie algebras.
Similar content being viewed by others
References
Arabyani, H.: Bounds for the dimension of the \(c\)-nilpotent multiplier of a pair of Lie algebras Bull. Iran. Math. Soc. 43(7), 2411–2418 (2017)
Arabyani, H., Saeedi, F.: On dimensions of derived algebra and central factor of a Lie algebra. Bull. Iran. Math. Soc. 41, 1093–1102 (2015)
Arabyani, H., Saeedi, F., Moghaddam, M.R.R., Khamseh, E.: Characterization of nilpotent Lie algebras pair by their Schur multipliers. Commun. Algebra 42, 5474–5483 (2014)
Arabyani, H., Safa, H.: Some properties of \(c\)-covers of a pair of Lie algebras. Quaest. Math. (2018). https://doi.org/10.2989/16073606.2018.1437482
Araskhan, M.: On the \(c\)-Covers and a special ideal of Lie algebras. Iran. J. Sci. Technol. Trans. A Sci. 40(3), 165–169 (2016)
Araskhan, M.: The dimension of the \(c\)-nilpotent multiplier. J. Algebra 386, 105–112 (2013)
Araskhan, M., Rismanchian, M.R.: Dimension of the \(c\)-nilpotent multiplier of Lie algebras. Proc. Indian Acad. Sci. (Math. Sci.) 126(3), 353–357 (2016)
Batten, P., Stitzinger, E.: On covers of Lie algebras. Commun. Algebra 24, 4301–4317 (1996)
Batten, P., Moneyhun, K., Stitzinger, E.: On characterizing nilpotent Lie algebras by their multipliers. Commun. Algebra 24, 4319–4330 (1996)
Bear, R.: Representation of groups as quotient groups, I, II and III. Trans. Am. Math. Soc. 58, 295–419 (1945)
Ellis, G.: The Schur multiplier of a pair of groups. Appl. Categ. Struct. 6, 355–371 (1998)
Karpilovsky, G.: The Schur Multiplier. Clarendon Press, Oxford (1987)
Moneyhun, K.: Isoclinisms in Lie algebras. Algebras Groups Geom. 11, 9–22 (1994)
Niroomand, P., Russo, F.: A note on the Schur multiplier of a nilpotent Lie algebra. Commun. Algebra 39, 1293–1297 (2011)
Rismanchian, M.R., Araskhan, M.: Some inequalities for the dimension of the Schur multiplier of a pair of (nilpotent) Lie algebras. J. Algebra 352, 173–179 (2012)
Rismanchian, M.R., Araskhan, M.: Some properties on the Schur multiplier of a pair of Lie algebras. J. Algebra Appl. 11, 1250011 (2012)
Robinson, D.J.S.: A Course in the Theory of Groups. Springer, New York (1982)
Saeedi, F., Salemkar, A.R., Edalatzadeh, B.: The commutator subalgebra and Schur multiplier of a pair of nilpotent Lie algebras. J. Lie Theory 21, 491–498 (2011)
Safa, H., Arabyan, H.: On \(c\)-nilpotent multiplier and \(c\)-covers of a pair of Lie algebras. Commun. Algebra 45, 4429–4434 (2017)
Salemkar, A.R., Alamian, V., Mohammadzadeh, H.: Some properties of the Schur multiplier and covers of Lie algebras. Commun. Algebra 36, 697–707 (2008)
Salemkar, A.R., Edalatzadeh, B., Araskhan, M.: Some inequalities for the dimension of the \(c\)-nilpotent multiplier of Lie algebras. J. Algebra 322, 575–1585 (2009)
Salemkar, A.R., Mirzaei, F.: Characterizing \(n\)-isoclinism classes of Lie algebras. Commun. Algebra 38, 3392–3403 (2010)
Schur, I.: Über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen. J. Reine Angew. Math. 127, 20–50 (1904)
Acknowledgements
The author would like to thank the referee for his/her comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Kailash C. Misra.
Rights and permissions
About this article
Cite this article
Arabyani, H. Some Results on the c-Nilpotent Multiplier of a Pair of Lie Algebras. Bull. Iran. Math. Soc. 45, 205–212 (2019). https://doi.org/10.1007/s41980-018-0126-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s41980-018-0126-6