• Corpus ID: 235266222

$EL_\infty$-algebras, Generalized Geometry, and Tensor Hierarchies

  title={\$EL\_\infty\$-algebras, Generalized Geometry, and Tensor Hierarchies},
  author={Leron Borsten and Hyungrok Kim and Christian Saemann},
We define a generalized form of L8-algebras called EL8-algebras. As we show, these provide the natural algebraic framework for generalized geometry and the symmetries of double field theory as well as the gauge algebras arising in the tensor hierarchies of gauged supergravity. Our perspective shows that the kinematical data of the tensor hierarchy is an adjusted higher gauge theory, which is important for developing finite gauge transformations as well as nonlocal descriptions. Mathematically… 

Figures and Tables from this paper



Duality Hierarchies and Differential Graded Lie Algebras

The algebraic structure allowing for consistent tensor hierarchies is proposed to be axiomatized by ‘infinity-enhanced Leibniz algebras’ defined on graded vector spaces generalizing Leibmars, and the structure can be reinterpreted as a differential graded Lie algebra.

The Embedding Tensor, Leibniz–Loday Algebras, and Their Higher Gauge Theories

We show that the data needed for the method of the embedding tensor employed in gauging supergravity theories are precisely those of a Leibniz algebra (with one of its induced quotient Lie algebras

Tensor hierarchy algebras and extended geometry. Part II. Gauge structure and dynamics

The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The

Tensor hierarchy algebras and extended geometry. Part I. Construction of the algebra

Tensor hierarchy algebras constitute a class of non-contragredient Lie superalgebras, whose finite-dimensional members are the “Cartan-type” Lie superalgebras in Kac’s classification. They have

Leibniz Gauge Theories and Infinity Structures

‘infinity-enhanced Leibniz algebras’ are defined that guarantee the existence of consistent tensor hierarchies to arbitrary level and can be used to define topological field theories for which all curvatures vanish.

Gauge Theories, Duality Relations and the Tensor Hierarchy

The complete 3- and 4-dimensional tensor hierarchies are computed, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations, thereby introducing additional scalars and a metric tensor.

Generalized higher gauge theory

A bstractWe study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is

The tensor hierarchy algebra

We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect

Tensor hierarchies and Leibniz algebras

The gauge structure of exceptional field theories and the tensor hierarchy

A bstractWe address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy