Abstract
In this paper, we first introduce the notion of an HLieDer triple, which includes a Hom-Lie algebra and a derivation. We define a cohomology theory for HLieDer triples with coefficients in a representation. We study central extensions of an HLieDer triple. Finally, we consider homotopy derivations on HLieb∞ algebras and 2-derivations on Hom-Lie 2-algebras, and we prove that the category of 2-term HLieb∞ algebras with homotopy derivations and the category of Hom-Lie 2-algebras with 2-derivations are equivalent.
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Acknowledgements
The paper is supported by NSFC (No. 12271292) and Guizhou Provincial Science and Technology Foundation (No. ZK[2023]025).
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Li, Y., Wang, D. Hom-Lie Algebras with Derivations. Front. Math 19, 535–550 (2024). https://doi.org/10.1007/s11464-022-0131-1
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DOI: https://doi.org/10.1007/s11464-022-0131-1