2024/09/03 by Anusuiya Baishya, Baishya, Anusuiya, Apurba Das +1
Mathematics · Medicine · #17B56 #17B61 #17B70 #Advanced Topics in Algebra #Cancer Treatment and Pharmacology #FOS: Mathematics #Ophthalmology and Eye Disorders #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2409.01865
openalex publication_date 2024/09/03 · openalex created_date 2024/09/29 · openalex updated_date 2026/07/28
In this paper, we introduce some new graded Lie algebras associated with a Hom-Lie algebra. At first, we define the cup product bracket and its application to the deformation theory of Hom-Lie algebra morphisms. We observe an action of the well-known Hom-analogue of the Nijenhuis-Richardson graded Lie algebra on the cup product graded Lie algebra. Using the corresponding semidirect product, we define the Frölicher-Nijenhuis bracket and study its application to Nijenhuis operators. We show that the Nijenhuis-Richardson graded Lie algebra and the Frölicher-Nijenhuis algebra constitute a matched pair of graded Lie algebras. Finally, we define another graded Lie bracket, called the derived bracket that is useful to study Rota-Baxter operators on Hom-Lie algebras.