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Nijenhuis operators on Leibniz algebras

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arxiv 2306.06428 v1 pith:K534AYCT submitted 2023-06-10 math.RA

Bibhash Mondal , Ripan Saha This is my paper · ORCID
classification math.RA
keywords algebrasleibniznijenhuisoperatorstheorycohomologydeformationdefine
verification ladder T0 review T1 audit T2 compute T3 formal
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In this paper, we study Nijenhuis operators on Leibniz algebras. We discuss the relationship of Nijenhuis operators with Rota-Baxter operators and modified Rota-Baxter operators on Leibniz algebras. We define a representation theory of Nijenhuis Leibniz algebras and construct a cohomology theory. Next, we define a one-parameter formal deformation theory of Nijenhuis Leibniz algebras and study infinitesimals, rigidity, and equivalences along the line of Gerstenhaber deformation theory. As an application of our cohomology theory, we show that our cohomology is deformation cohomology and study abelian extensions of such algebras.

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Cited by 1 Pith paper

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  1. Crossed modules of ternary Leibniz algebras

    math.RA 2025-01 reject novelty 4.0 of 10

    The paper transfers crossed modules from triassociative and Leibniz algebras to ternary Leibniz algebras, but omits the supporting computations and contains garbled formulas.

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