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Superalgebras, constraints and partition functions
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We consider Borcherds superalgebras obtained from semisimple finite-dimensional Lie algebras by adding an odd null root to the simple roots. The additional Serre relations can be expressed in a covariant way. The spectrum of generators at positive levels are associated to partition functions for a certain set of constrained bosonic variables, the constraints on which are complementary to the Serre relations in the symmetric product. We give some examples, focusing on superalgebras related to pure spinors, exceptional geometry and tensor hierarchies, of how construction of the content of the algebra at arbitrary levels is simplified.
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Cited by 2 Pith papers
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Tensor hierarchy algebras and extended geometry II: Gauge structure and dynamics
The gauge structure and pseudo-action of extended geometry with ancillary transformations are encoded by a tensor hierarchy algebra S(g+), yielding a partial L-infinity description for finite-dimensional structure groups.
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Tensor hierarchy algebras and extended geometry I: Construction of the algebra
This paper constructs tensor hierarchy algebras W(g+) and S(g+) for Kac-Moody extensions of finite-dimensional simply laced Lie algebras and gives their local module content, with a companion representation identity t...
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