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Oxidizing Borcherds symmetries

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arxiv 1301.1346 v1 pith:LA3NM6KX submitted 2013-01-07 hep-th math.RA

Axel Kleinschmidt , Jakob Palmkvist This is my paper · ORCID
classification hep-thmath.RA
keywords borcherdshierarchytensoralgebraalgebrasconstructeddimensionsalgebraic
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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.

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