Hom-Lie Algebras with Derivations

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 o...

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Bibliographic Details
Published in:Frontiers of Mathematics 2024-05, Vol.19 (3), p.535-550
Main Authors: Li, Yizheng, Wang, Dingguo
Format: Article
Language:English
Subjects:
Algebra
Derivation
Homology
Lie groups
Mathematics
Mathematics and Statistics
Research Article
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Summary: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.
ISSN:2731-8648
1673-3452
2731-8656
1673-3576
DOI:10.1007/s11464-022-0131-1