A study of infinite dimensional algebraic groups and Lie algebras, and an application to words and sequences

在秩为2的双曲Kac-Moody群具有平凡对易关系的情形下，得到了某些无限域上的群是模中心单群.也就是说，如果我们假设秩为2的双曲Cartan矩阵没有-1元素，并且如果我们选择有限域的代数闭包，那么我们可以得到我们的群的简单性。我们还对局部仿射李代数进行了分类。此外，我们还证明了基本自动机和数的层次之间有一个有趣的对应关系。

In the case when rank 2 hyperbolic Kac-Moody groups have trivial commutation relations, we obtained that the groups over certain infinite fields are simple modulo their centers. That is, if we suppose that a rank 2 hyperbolic Cartan matrix has no -1 entry, and if we choose the algebraic closure of a finite field, then we can obtain the simplicity of our group. We also classified the locally affine Lie algebras. Furthermore, we showed that there is an interesting correspondence between fundamental automata and hierarchy of numbers.