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- W3102007391 abstract "We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for D between 3 and 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D-2-p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor." @default.
- W3102007391 created "2020-11-23" @default.
- W3102007391 creator A5064714865 @default.
- W3102007391 date "2014-01-01" @default.
- W3102007391 modified "2023-09-25" @default.
- W3102007391 title "The tensor hierarchy algebra" @default.
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- W3102007391 doi "https://doi.org/10.1063/1.4858335" @default.
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