A research on algebraic groups and Kac-Moody groups, and their applications

(1)给出了U_q(Sl_2)的一个新公式，并给出了它的表示为可积的一个充分条件.(2)我们证明了扩展仿射李代数的所谓Kac猜想.(3)我们引入了一些与给定的一维分片有关的双代数，(4)我们构造了一些伴随零度为2的完备扩张仿射李代数的伴随群的泛中心扩张。(5)证明了由一维切片定义的群和李代数都有标准的和加性的Gauss分解。(6)我们证明了域上UFD代数的sl_2的许多共轭定理，特别是对于Cartan子代数和TDS的共轭定理。

(1) We introduced a new formulas for U q(sl_2), and gave a sufficient condition for its representation to be integrable.(2) We gave a proof of the so-called Kac-conjecture for extended affine Lie algebras.(3) We introduced certain bialgebras associated with given one-dimensional tilings, and gave a characterization for such tilings to be locally indistinguishable using our bialgebras.(4) We constructed universal central extensions of certain adjoint groups associated with completed extended affine Lie algebras with nullity 2.(5) We showed the fact that the groups and Lie algebras defined by one-dimensional tilings have standard and additive Gauss decompositions.(6) We proved many conjugacy theorems for sl_2 of UFD algebras over fields, especially for Cartan subalgebras and for TDS as some analogue of Jacobson-Morozov theorem.