Simultaneous mutually commuting coset Virasoro actions are realized on the tensor algebra of the Feingold-Frenkel algebra, giving explicit decompositions and tensor ground states up to level five.
Teleparallel Geroch geometry
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We construct the teleparallel dynamics for extended geometry where the structure algebra is (an extension of) an untwisted affine Kac-Moody algebra. This provides a geometrisation of the Geroch symmetry appearing on dimensional reduction of a gravitational theory to two dimensions. The formalism is adapted to the underlying tensor hierarchy algebra, and will serve as a stepping stone towards the geometrisation of other infinite-dimensional, e.g. hyperbolic, symmetries.
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From Tensor Algebras to Hyperbolic Kac-Moody Algebras
Simultaneous mutually commuting coset Virasoro actions are realized on the tensor algebra of the Feingold-Frenkel algebra, giving explicit decompositions and tensor ground states up to level five.