论文标题
自态谎言代数和相应的集成系统
Automorphic Lie algebras and corresponding integrable systems
论文作者
论文摘要
我们研究自动谎言代数及其在可集成系统中的应用。当自动形态不是循环的情况下，自然而然地对著名的kac-moody代数的自然概括是对著名的kac-moody代数的自然概括。它们是无限的尺寸，几乎是分级的。我们制定了分级同构的概念，并对基于所有有限减少组的$ sl（2，c）$ sutmorthic Lie代数分类。我们表明，可以自然地根据自动形态谎言代数来自然制定整合系统的层次结构。
We study automorphic Lie algebras and their applications to integrable systems. Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to the case when the group of automorphisms is not cyclic. They are infinite dimensional and almost graded. We formulate the concept of a graded isomorphism and classify $sl(2,C)$ based automorphic Lie algebras corresponding to all finite reduction groups. We show that hierarchies of integrable systems, their Lax representations and master symmetries can be naturally formulated in terms of automorphic Lie algebras.
