Tensor hierarchy algebras and extended geometry. Part I. Construction of the algebra
Journal article, 2020

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 applications in mathematical physics, especially in extended geometry and gauged supergravity. We further develop the recently proposed definition of tensor hierarchy algebras in terms of generators and relations encoded in a Dynkin diagram (which coincides with the diagram for a related Borcherds superalgebra). We apply it to cases where a grey node is added to the Dynkin diagram of a rank r + 1 Kac-Moody algebra g(+), which in turn is an extension of a rank r finite-dimensional semisimple simply laced Lie algebra g. The algebras are specified by g together with a dominant integral weight lambda. As a by-product, a remarkable identity involving representation matrices for arbitrary integral highest weight representations of g is proven. An accompanying paper [1] describes the application of tensor hierarchy algebras to the gauge structure and dynamics in models of extended geometry.


Gauge Symmetry

Space-Time Symmetries

Differential and Algebraic Geometry


Martin Cederwall

Chalmers, Physics, Subatomic, High Energy and Plasma Physics

Jakob Palmkvist

Chalmers, Mathematical Sciences, Algebra and geometry

Chalmers, Physics, Theoretical Physics

Journal of High Energy Physics

1126-6708 (ISSN) 1029-8479 (eISSN)

Vol. 2020 2 144

Subject Categories

Algebra and Logic


Other Physics Topics

Mathematical Analysis



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Latest update

4/6/2022 1