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<p>In this paper, we introduce the concept of the <i>c</i>-nilpotent multiplier of Leibniz algebras. Also, we obtain some bounds for the dimension of the nilpotent multiplier of finite dimensional Leibniz algebras. Also, we determine the structure of the <i>c</i>-nilpotent multiplier of a direct sum of Leibniz algebras. Moreover, we tie this concept to the <i>c</i>-capability of Leibniz algebras to determine nilpotent multiplier of some extra-special Leibniz algebras. We apply these results and a version of the Witt’s formula for Leibniz algebras to obtain the dimension of the nilpotent multiplier of some Leibniz algebras.</p>

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The Nilpotent Multiplier of Leibniz Algebras

  • 期刊论文

  • 发表日期：

    2025年8月28日

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  • Abbas Asadi,
  • Mehdi Araskhan,
  • Behrouz Edalatzadeh,
  • Shahram Heidarian

摘要

In this paper, we introduce the concept of the c-nilpotent multiplier of Leibniz algebras. Also, we obtain some bounds for the dimension of the nilpotent multiplier of finite dimensional Leibniz algebras. Also, we determine the structure of the c-nilpotent multiplier of a direct sum of Leibniz algebras. Moreover, we tie this concept to the c-capability of Leibniz algebras to determine nilpotent multiplier of some extra-special Leibniz algebras. We apply these results and a version of the Witt’s formula for Leibniz algebras to obtain the dimension of the nilpotent multiplier of some Leibniz algebras.