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Tensor Hierarchy Algebra Extensions of Over-Extended Kac-Moody Algebras
Department of Physics, Chalmers University of Technology, Gothenburg, Sweden.
Örebro University, School of Science and Technology. Department of Mathematics.
2022 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 389, no 1, p. 571-620Article in journal (Refereed) Published
Abstract [en]

Tensor hierarchy algebras are infinite-dimensional generalisations of Cartantype 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 role 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 L-1. A conjecture about the complete superalgebra is formulated, relating it to the corresponding Borcherds superalgebra.

Place, publisher, year, edition, pages
Springer, 2022. Vol. 389, no 1, p. 571-620
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:oru:diva-95978DOI: 10.1007/s00220-021-04243-3ISI: 000726001100001Scopus ID: 2-s2.0-85120541142OAI: oai:DiVA.org:oru-95978DiVA, id: diva2:1620584
Note

Funding agency:

University of Geneva

Available from: 2021-12-16 Created: 2021-12-16 Last updated: 2022-02-02Bibliographically approved

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Palmkvist, Jakob

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