Compatible $L_\infty$-algebras

DOI10.1016/J.JALGEBRA.2022.07.020arXiv2111.13306MaRDI QIDQ6383990

Apurba Das

Publication date: 25 November 2021

Abstract: A compatible $L_{i}nfty$-algebra is a graded vector space together with two compatible $L_{i}nfty$-algebra structures on it. Given a graded vector space, we construct a graded Lie algebra whose Maurer-Cartan elements are precisely compatible $L_{i}nfty$-algebra structures on it. We provide examples of compatible $L_{i}nfty$-algebras arising from Nijenhuis operators, compatible $V$-datas and compatible Courant algebroids. We define the cohomology of a compatible $L_{i}nfty$-algebra and as an application, we study formal deformations. Next, we classify `strict' and `skeletal' compatible $L_{i}nfty$-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 $L_{i}nfty$-algebras.

Mathematics Subject Classification ID

Cohomology of Lie (super)algebras (17B56) Homotopical algebra, Quillen model categories, derivators (18N40) Categorification (18N25)

This page was built for publication: Compatible $L_\infty$-algebras

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6383990)