Biderivations of some classes of solvable Leibniz algebras

2025/07/24 by Bakhtiyor Yusupov, Yusupov, Bakhtiyor, Doston Jumaniyozov +2
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2507.18134

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

In this work, we investigate anti-derivations and biderivation of Leibniz algebras. We describe general form of anti-derivations and biderivations on null-filiform and filiform Leibniz algebras. Moreover, we show how to construct Leibniz algebras, while using these biderivations. We describe general form of anti-derivations and biderivations on solvable Leibniz algebras with null-filiform and filiform nilradicals. Interesting fact that, any biderivations of solvable Leibniz algebras with null-filiform and filiform nilradicals are inner biderivations.

Citations

• Computational Methods for Biderivations of 4-dimensional nilpotent complex leibniz algebras
• Some irreducible components of the variety of complex n+1-dimensional Leibniz algebras
• Classification of solvable Leibniz algebras with naturally graded filiform nilradical
• Classification of solvable Leibniz algebras with null-filiform nilradical
• Biderivations of the Parabolic Subalgebras of Simple Lie Algebras
• Centralizing Maps in Prime Rings with Involution

Related

• Biderivations of complete Leibniz algebras
• Computational Methods for Biderivations of 4-dimensional nilpotent complex leibniz algebras
• Classification of solvable Leibniz algebras with null-filiform nilradical
• Solvable Leibniz algebras with filiform nilradical
• Solvable Leibniz algebras whose nilradical is a quasi-filiform Leibniz algebra of maximum length