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.

M-Theory

Differential and Algebraic Geometry

Space-Time Symmetries

Gauge Symmetry

Author

Martin Cederwall

Chalmers, Physics, Subatomic, High Energy and Plasma Physics

Jakob Palmkvist

Chalmers, Physics, Theoretical Physics

Chalmers, Mathematical Sciences, Algebra and geometry

Journal of High Energy Physics

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

2 144

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1007/JHEP02(2020)144

More information

Latest update

7/15/2020