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We particularise the construction of generalised Kac-Moody algebras associated to compact real manifolds to the case of the two-torus \(\mathbb T_2\) and the two-sphere \({\mathbb S}^2\) . It is shown that these algebras, as well as a Virasoro algebra associated to the two-torus and the two-sphere, can also be derived considering the usual Kac-Moody and Virasoro algebras.

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Kac-Moody and Virasoro Algebras on the Two-Sphere and the Two-Torus

  • 会议论文

  • 发表日期：

    2025年

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  • Rutwig Campoamor-Stursberg,
  • Michel Rausch de Traubenberg

摘要

We particularise the construction of generalised Kac-Moody algebras associated to compact real manifolds to the case of the two-torus \(\mathbb T_2\) and the two-sphere \({\mathbb S}^2\) . It is shown that these algebras, as well as a Virasoro algebra associated to the two-torus and the two-sphere, can also be derived considering the usual Kac-Moody and Virasoro algebras.