2020/04/16 by Apurba Das, Das, Apurba
Mathematics · Physics and Astronomy · #17B10 #17B38 #17B40 #17B56 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math-ph #math.MP #math.RA #math.RT #msc:17B10 #msc:17B38 #msc:17B40 #msc:17B56
paper · pdf · doi:10.48550/arxiv.2004.07497
18 pages; Comments are welcome
arxiv created 2020/04/16 · openalex publication_date 2020/04/16 · arxiv updated 2020/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of O-operators on modules over Lie algebras generalize Rota-Baxter operators. They also generalize Poisson structures on Lie algebras in the presence of modules. Motivated from Poisson structures, we define gauge transformations and reductions of O-operators. Next we consider compatible O-operators on modules over Lie algebras. We define ON-structures which give rise to hierarchy of compatible O-operators. We show that a solution of the strong Maurer-Cartan equation on a twilled Lie algebra associated to an O-operator gives rise to an ON-structure, hence, a hierarchy of compatible O-operators. Finally, we also introduce generalized complex structures and holomorphic O-operators on modules over Lie algebras and show how they incorporate O-operators.