Some properties of the c-nilpotent multiplier of a pair of Lie algebras

Homayoon Arabyani ()
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Homayoon Arabyani: Islamic Azad University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 2, 557-564

Abstract: Abstract The concept of the Schur multiplier of a Lie algebra was introduced by Batten et al. (1996). This concept was extended to that of a c-nilpotent multiplier of a Lie algebra, and then further extended to a theory of a c-nilpotent multiplier of a pair of Lie algebras, by the author and others. In this paper we present some new inequalities for the dimension of the c-nilpotent multiplier of a pair of Lie algebras. We also give a necessary and sufficient condition for the c-nilpotent multiplier of a pair of Lie algebras to embed into the c-nilpotent multiplier of their quotient. Finally we provide a sufficient condition for the c-nilpotent multiplier of a pair of Lie algebras to be finite dimensional.

Keywords: Pair of Lie algebras; c-nilpotent multiplier; 17B30; 17B99 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0416-6

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