Tensor hierarchy algebra extensions of over-extended Kac--Moody algebras

Abstract

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 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.

66 pages. v2: several minor changes. Title changed. Version accepted for publication in Communications in Mathematical Physics

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Cited by in corpus (6)

• Maximal D=2 supergravities from higher dimensions
• Teleparallelism in the algebraic approach to extended geometry
• The E10 Wheeler-DeWitt operator at low levels
• Extended geometry of magical supergravities
• The teleparallel complex
• Unfolding $E_{11}$