中科院吴文俊数学重点实验室吴文俊讲座报告

发布者:系统管理员发布时间:2012-02-20浏览次数:9

题  目:Poisson algebras and Jacobi pairs


报告人:苏育才教授   上海同济大学数学学院


时  间:2012年2月23日下午3:00--4:00
地  点:管理科研楼1518


摘  要:In this talk, we discuss the natural Poisson algebra structure (P,[.,.],.) on the space P = C[y]((x^{-1/N})) for some sufficient large N, and introduce some automorphisms of P which are products of the automorphisms of forms e^{ad_H}. These automorphisms are used to study some properties of Jacobi pairs in P. In particular, starting from a Jacobi pair (F,G) in C[x,y] which violates the two-dimensional Jacobian conjecture, by applying some variable changes,  we obtain a pair still denoted by (F,G) in C[x^{/pm1/N},y] with the form F=x^{m/(m+n)}(f+F_0), G=x^{n/(m+n)}(g+G_0) for some positive integers m,n, and f,g in C[y], F_0,G_0 in x^{-1/N} C[x^{-1/N},y], such that F,G satisfy some additional conditions. We also generalize some results to the Weyl algebra W = C[v]((u^{-1/N})) with relation [u,v] = 1, and obtain some properties of pairs (F,G) satisfying [F,G] = 1, referred to as Dixmier pairs.


主办单位:0029cc金沙贵宾会     中科院吴文俊数学重点实验室

欢迎感兴趣的师生参加!