Continuum Kac-Moody algebras
| Autor: | Andrea Appel, Francesco Sala, Olivier Schiffmann |
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| Rok vydání: | 2018 |
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| DOI: | 10.48550/arxiv.1812.08528 |
| Popis: | We introduce a new class of infinite-dimensional Lie algebras, which we refer to as continuum Kac-Moody algebras. Their construction is closely related to that of usual Kac-Moody algebras, but they feature a continuum root system with no simple roots. Their Cartan datum encodes the topology of a one-dimensional real space and can be thought of as a generalization of a quiver, where vertices are replaced by connected intervals. For these Lie algebras, we prove an analogue of the Gabber-Kac-Serre theorem, providing a complete set of defining relations featuring only quadratic Serre relations. Moreover, we provide an alternative realization as continuum colimits of symmetric Borcherds-Kac-Moody algebras with at most isotropic simple roots. The approach we follow deeply relies on the more general notion of a semigroup Lie algebra and its structural properties. Comment: Final version. Minor changes. Technical proofs moved to Appendix. Prop. 6.13 corrected. 42 pages. To appear in the Moscow Mathematical Journal |
| Databáze: | OpenAIRE |
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