Tensor Hierarchy Algebra Extensions of Over-Extended Kac–Moody Algebras
Artikel i vetenskaplig tidskrift, 2022

Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They are not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus of attention due to the fundamental rôle they play for extended geometry. In the present paper, we examine tensor hierarchy algebras which are super-extensions of over-extended (often, hyperbolic) Kac–Moody algebras. They contain novel algebraic structures. Of particular interest is the extension of a over-extended algebra by its fundamental module, an extension that contains and generalises the extension of an affine Kac–Moody algebra by a Virasoro derivation L1. A conjecture about the complete superalgebra is formulated, relating it to the corresponding Borcherds superalgebra.


Martin Cederwall

Chalmers, Fysik, Subatomär, högenergi- och plasmafysik

Jakob Palmkvist

Örebro universitet

Communications in Mathematical Physics

0010-3616 (ISSN) 1432-0916 (eISSN)

Vol. 389 1 571-620


Algebra och logik


Matematisk analys



Mer information

Senast uppdaterat