Automorphic Lie Algebras and Modular Forms
Automorphic Lie Algebras and Modular Forms
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自守李代数和模形式
DOI：
10.1093/imrn/rnab376
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发表时间：
2023
影响因子：
1
通讯作者：
Knibbeler V
中科院分区：
文献类型：
--
作者：
Knibbeler V
引入并研究了与模群相关的自同构李代数的双曲型。设复简单李代数上具有作用的有限索引子群，可推广为。证明了对应值模形式的李代数与一般模形式的扩展是同构的。这建立了Kac在扭环代数上的一个著名结果的模模拟。主同余子群的情况，在克莱因和弗里克的经典结果和著名的马尔可夫丢芬图方程的关系中被更详细地考虑。最后，我们简要地讨论了这些李代数的扩展和表示。
We introduce and study certain hyperbolic versions of automorphic Lie algebras related to the modular group. Letbe a finite index subgroup ofwith an action on a complex simple Lie algebra, which can be extended to. We show that the Lie algebra of the corresponding-valued modular forms is isomorphic to the extension ofover the usual modular forms. This establishes a modular analogue of a well-known result by Kac on twisted loop algebras. The case of principal congruence subgroups, is considered in more detail in relation to the classical results of Klein and Fricke and the celebrated Markov Diophantine equation. We finish with a brief discussion of the extensions and representations of these Lie algebras.