Nonabelian embedding tensors
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Publication:6395806
DOI10.1007/S11005-023-01637-3arXiv2204.02584MaRDI QIDQ6395806
Publication date: 6 April 2022
Abstract: In this paper, first we introduce the notion of a nonabelian embedding tensor, which is a nonabelian generalization of an embedding tensor. Then we introduce the notion of a Leibniz-Lie algebra, which is the underlying algebraic structure of a nonabelian embedding tensor, and can also be viewed as a nonabelian generalization of a Leibniz algebra. Next using the derived bracket, we construct a differential graded Lie algebra, whose Maurer-Cartan elements are exactly nonabelian embedding tensors. Consequently, we obtain the differential graded Lie algebra that governs deformations of a nonabelian embedding tensor. Finally, we define the cohomology of a nonabelian embedding tensor and use the second cohomology group to characterize linear deformations.
Automorphisms, derivations, other operators for Lie algebras and super algebras (17B40) Cohomology of Lie (super)algebras (17B56) Leibniz algebras (17A32) Yang-Baxter equations and Rota-Baxter operators (17B38)
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