Lie algebras with differential operators of any weights

In this paper, we define a cohomology theory for differential Lie algebras of any weight. As applications of the cohomology, we study abelian extensions and formal deformations of differential Lie algebras of any weight. Finally, we consider homotopy differential operators on $ \mathrm{L}_{\infty} $...

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Bibliographic Details
Published in:Electronic research archive 2023, Vol.31 (3), p.1195-1211
Main Authors: Li, Yizheng, Wang, Dingguo
Format: Article
Language:English
Subjects:
cohomology
deformation
derivation
extension
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Summary:In this paper, we define a cohomology theory for differential Lie algebras of any weight. As applications of the cohomology, we study abelian extensions and formal deformations of differential Lie algebras of any weight. Finally, we consider homotopy differential operators on $ \mathrm{L}_{\infty} $ algebras and 2-differential operators of any weight on Lie 2-algebras, and we prove that the category of 2-term $ \mathrm{L}_{\infty} $ algebras with homotopy differential operators of any weight is same as the category of Lie 2-algebras with 2-differential operators of any weight.
ISSN:2688-1594
2688-1594
DOI:10.3934/era.2023061