Lie algebras with differential operators of any weights

Yizheng Li; Dingguo Wang; Yizheng Li; Dingguo Wang

doi:10.3934/era.2023061

Electronic Research Archive

2023, Volume 31, Issue 3: 1195-1211. doi: 10.3934/era.2023061

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Research article

Lie algebras with differential operators of any weights

Yizheng Li ,
Dingguo Wang ^,

School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Received: 26 October 2022 Revised: 08 December 2022 Accepted: 19 December 2022 Published: 28 December 2022

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.
- cohomology,
- extension,
- deformation,
- derivation
Citation: Yizheng Li, Dingguo Wang. Lie algebras with differential operators of any weights[J]. Electronic Research Archive, 2023, 31(3): 1195-1211. doi: 10.3934/era.2023061

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Abstract

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.

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