Mathematical Sciences: Noncommutative Algebras

本研究主要研究某些非交换代数的结构。主要关注的是作为Weyl代数的不动环的变形而产生的代数的结构。用来研究这些代数的技术涉及到李代数理论和代数几何思想的相互交织。主要研究者还将继续研究包络代数，重点研究计算半单李代数的包络代数的本原因子的K-理论的问题。非对易环理论代表了对具有加法和非对易乘法的代数结构的研究。K-理论代表了向量空间和线性映射的演化代数理论。本课题主要研究某些非对易环的结构、K-理论和状态空间。

This research is concerned with the structure of certain noncommutative algebras. The main concern is the structure of algebras which arise as deformations of fixed rings of the Weyl algebras. The techniques used to study these algebras involve the intertwining of ideas from the theory of Lie algebras and algebraic geometry. The principle investigator will also pursue the study of enveloping algebras, focusing on the problem of calculating the K-theory of primitive factors of the enveloping algebra of a semi-simple Lie algebra. Noncommutative ring theory represents the study of an algebraic structure possessing an addition and a noncommutative multiplication. K-theory represents the evolved algebraic theory of vector spaces and linear mappings. This project is concerned with the structure, K-theory and state-space of certain noncommutative rings.