Upper bounds on the dimension of the Schur Lie-multiplier of Lie-nilpotent Leibniz n-algebras

Authors

• Narcisse G.Bell Bogmis, University of Dschang
• Guy R. Biyogmam, Georgia College & State University
• Hesam Safa, University of Bojnord, Iran
• Calvin Tcheka, University of Dschang

Document Type

Article

Publication Date

1-1-2025

Publication Title

Communications in Algebra

Abstract

The Schur (Formula presented.) -multiplier of Leibniz algebras is the Schur multiplier of Leibniz algebras defined relative to the Liezation functor. In this paper, we study upper bounds for the dimension of the Schur (Formula presented.) -multiplier of (Formula presented.) -filiform Leibniz n-algebras and the Schur (Formula presented.) -multiplier of its (Formula presented.) -central factor. The upper bound obtained is associated to both the sequences of central binomial coefficients and the sum of the numbers located in the rhombus part of Pascal’s triangle. Also, the pattern of counting the number of (Formula presented.) -brackets of a particular Leibniz n-algebra leads us to a new property of Pascal’s triangle. Moreover, we discuss some results which improve the existing upper bound for m-dimensional (Formula presented.) -nilpotent Leibniz n-algebras with d-dimensional (Formula presented.) -commutator. In particular, it is shown that if (Formula presented.) is an m-dimensional (Formula presented.) -nilpotent Leibniz 2-algebra with one-dimensional (Formula presented.) -commutator, then (Formula presented.).

Volume Number

53

Issue Number

8

First Page

3144

Last Page

3156

DOI

10.1080/00927872.2025.2455456

Recommended Citation

Bogmis, Narcisse G.Bell; Biyogmam, Guy R.; Safa, Hesam; and Tcheka, Calvin, "Upper bounds on the dimension of the Schur Lie-multiplier of Lie-nilpotent Leibniz n-algebras" (2025). Faculty and Staff Works. 958.
https://kb.gcsu.edu/fac-staff/958