Nonabelian embedding tensors

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.

References in corpus (4)

• E(11) and the Embedding Tensor
• Multiple M2-branes and the Embedding Tensor
• The controlling $L_{\infty }$-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples
• Maximal Nine Dimensional Supergravity, General gaugings and the Embedding Tensor

Cited by in corpus (2)

• Cohomology and deformations of nonabelian embedding tensors between Lie triple systems
• Nonabelian embedding tensors on 3-Lie algebras and 3-Leibniz-Lie algebras