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

Author

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  • Homayoon Arabyani

    (Islamic Azad University)

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.

Suggested Citation

  • Homayoon Arabyani, 2020. "Some properties of the c-nilpotent multiplier of a pair of Lie algebras," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 557-564, June.
  • Handle: RePEc:spr:indpam:v:51:y:2020:i:2:d:10.1007_s13226-020-0416-6
    DOI: 10.1007/s13226-020-0416-6
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