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- W3016776145 abstract "The notion of $mathcal{O}$-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 $mathcal{O}$-operators. Next we consider compatible $mathcal{O}$-operators on modules over Lie algebras. We define $mathcal{ON}$-structures which give rise to hierarchy of compatible $mathcal{O}$-operators. We show that a solution of the strong Maurer-Cartan equation on a twilled Lie algebra associated to an $mathcal{O}$-operator gives rise to an $mathcal{ON}$-structure, hence, a hierarchy of compatible $mathcal{O}$-operators. Finally, we also introduce generalized complex structures and holomorphic $mathcal{O}$-operators on modules over Lie algebras and show how they incorporate $mathcal{O}$-operators." @default.
- W3016776145 created "2020-04-24" @default.
- W3016776145 creator A5086304050 @default.
- W3016776145 date "2020-04-16" @default.
- W3016776145 modified "2023-09-27" @default.
- W3016776145 title "On $mathcal{O}$-operators on modules over Lie algebras" @default.
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