Tensor Hierarchy Algebra Extensions of Over-Extended Kac–Moody Algebras
Journal article, 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.

Author

Martin Cederwall

Chalmers, Physics, Subatomic, High Energy and Plasma Physics

Jakob Palmkvist

Örebro University

Communications in Mathematical Physics

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

Vol. 389 1 571-620

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.1007/s00220-021-04243-3

More information

Latest update

4/5/2022 5