Study of infinite dimensional algebraic groups and Lie algebras, and applications to material science and life science

研究了无穷维代数群和李代数的一些结构。特别是研究了某些双曲型Kac-Moody群，给出了局部仿射李代数的分类。建立了有限和无限字母序列的代数理论，并找到了控制这些序列的代数方法。在准晶体作为材料科学和DNA序列作为生命科学方面已经建立了一些有用的数学应用。

Some structures of infinite dimensional algebraic groups and Lie algebras have been studied. Especially, certain hyperbolic type Kac-Moody groups have been studied, and the classification of locally affine Lie algebras has been given. Algebraic theory related to finite and infinite sequences of letters has been created, and some algebraic method to control those sequences was found. Some useful mathematical applications to quasicrystals as material science and DNA sequences as life science have been constructed.