标题： 关于自守李代数的分类 显示英文标题

标题： On the Classification of Automorphic Lie Algebras

摘要： 证明了可以使用不变量理论以统一的方式表述约简问题。 这提供了一个强大的分析工具，并为这些代数在可积系统之外的新应用开辟了道路。 此外，证明了与二十面体群I、八面体群O、四面体群T和二面体群Dn相关的sl2-自同构李代数是同构的。 该证明基于经典不变量理论的技术，并利用了Clebsch-Gordan分解和转置量、Molien函数和迹形式。 这一结果在选择相同的群表示时，提供了与有限群相关的sl2-自同构李代数的完整分类，这是实现自同构李代数完整分类的关键一步。 显示英文摘要

摘要： It is shown that the problem of reduction can be formulated in a uniform way using the theory of invariants. This provides a powerful tool of analysis and it opens the road to new applications of these algebras, beyond the context of integrable systems. Moreover, it is proven that sl2-Automorphic Lie Algebras associated to the icosahedral group I, the octahedral group O, the tetrahedral group T, and the dihedral group Dn are isomorphic. The proof is based on techniques from classical invariant theory and makes use of Clebsch-Gordan decomposition and transvectants, Molien functions and the trace-form. This result provides a complete classification of sl2-Automorphic Lie Algebras associated to finite groups when the group representations are chosen to be the same and it is a crucial step towards the complete classification of Automorphic Lie Algebras.