Tensor hierarchies and Leibniz algebras

Abstract

Tensor hierarchies are algebraic objects that emerge in gauging procedures in supergravity models, and that present a very deep and intricate relationship with Leibniz (or Loday) algebras. In this paper, we show that one can canonically associate a tensor hierarchy to any Loday algebra. By formalizing the construction that is performed in supergravity, we build this tensor hierarchy explicitly. We show that this tensor hierarchy can be canonically equipped with a differential graded Lie algebra structure that coincides with the one that is found in supergravity theories.

v6. (important typo corrected), 53 pages, final version

References in corpus (10)

• Lectures on Gauged Supergravity and Flux Compactifications
• Gauged Supergravities
• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
• Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
• Higher derived brackets
• Leibniz-Chern-Simons Theory and Phases of Exceptional Field Theory
• Tensor Hierarchies of 5- and 6-Dimensional Field Theories
• Higher Gauge Structures in Double and Exceptional Field Theory
• Non-abelian Gerbes and Enhanced Leibniz Algebras
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Cited by in corpus (14)

• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
• Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
• Towards an M5-Brane Model II: Metric String Structures
• The controlling $L_{\infty }$-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples
• Infinity-enhancing of Leibniz algebras
• From Lie algebra crossed modules to tensor hierarchies
• Nonabelian embedding tensors
• Higher curvature Bianchi identities, generalised geometry and $L_{\infty }$ algebras
• Classical worldvolumes as generalised geodesics
• The $L_{\infty }$-algebra of the S-matrix
• Nonlinear realisations of Lie superalgebras
• Dg Loday-Pirashvili modules over Lie algebras
• The canonical formulation of E${}_{6(6)}$ exceptional field theory
• $E_2{L}_{\infty }$-algebras, Generalized Geometry, and Tensor Hierarchies