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High Energy Physics - Theory, hep-th,Mathematics, Rings and Algebras, math.RA
Abstract:
The tensor hierarchy of maximal supergravity in D dimensions is known to be
closely related to a Borcherds (super)algebra that is constructed from the
global symmetry group E(11-D). We here explain how the Borcherds algebras in
different dimensions are embedded into each other and can be constructed from a
unifying Borcherds algebra. The construction also has a natural physical
explanation in terms of oxidation. We then go on to show that the Hodge duality
that is present in the tensor hierarchy has an algebraic counterpart. For D>8
the Borcherds algebras we find differ from the ones existing in the literature
although they generate the same tensor hierarchy.
