Tensor Hierarchy Algebra Extensions of Over-Extended Kac–Moody Algebras

Abstract Tensor hierarchy algebras are infinite-dimensional generalisations of Cartan-type Lie superalgebras. They not contragredient, exhibiting an asymmetry between positive and negative levels. These superalgebras have been a focus attention due to the fundamental rôle they play for extended geometry. In present paper, we examine tensor which super-extensions over-extended (often, hyperbolic) Kac–Moody algebras. contain novel algebraic structures. Of particular interest is extension algebra by its module, that contains generalises affine Virasoro derivation $$L_1$$ L 1 . A conjecture about complete superalgebra formulated, relating it corresponding Borcherds superalgebra.