The Argument Shift Method in Universal Enveloping Algebra Ugl_d
发布时间：2023年09月25日
浏览次数：1893
发布者: Wenqiong Li
主讲人： Georgy Igorevich Sharygin (Moscow State University)
活动时间： 从 2023-09-26 14:00 到 15:00
场地： 北京国际数学研究中心，全斋全29教室
We prove the conjecture that allows one extend the argument shifting procedure from symmetric algebra Sgl_d of the Lie algebra gl_d to the universal enveloping algebra Ugl_d. Namely, it turns out that the iterated quasi-derivations of the central elements in Ugl_d commute with each other. Here quasi-derivation is a linear operator on Ugld, constructed by Gurevich, Pyatov and Saponov. This allows one better understand the structure of the quantum argument shift algebras (or the quantum Mishchenko-Fomenko algebras) in the universal enveloping algebra of gl_d. In the end I will briefly describe the methods that allow one to partially extend this result to other classical series of simple Lie algebras. Based on a joint work with Y. Ikeda and A. Molev.
