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- W3216184080 abstract "A compatible $L_infty$-algebra is a graded vector space together with two compatible $L_infty$-algebra structures on it. Given a graded vector space, we construct a graded Lie algebra whose Maurer-Cartan elements are precisely compatible $L_infty$-algebra structures on it. We provide examples of compatible $L_infty$-algebras arising from Nijenhuis operators, compatible $V$-datas and compatible Courant algebroids. We define the cohomology of a compatible $L_infty$-algebra and as an application, we study formal deformations. Next, we classify `strict' and `skeletal' compatible $L_infty$-algebras in terms of crossed modules and cohomology of compatible Lie algebras. Finally, we introduce compatible Lie $2$-algebras and find their relationship with compatible $L_infty$-algebras." @default.
- W3216184080 created "2021-12-06" @default.
- W3216184080 creator A5086304050 @default.
- W3216184080 date "2021-11-26" @default.
- W3216184080 modified "2023-09-27" @default.
- W3216184080 title "Compatible $L_infty$-algebras" @default.
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