勷勤数学•杰出学者报告

题      目：Tame and wild automorphisms of free algebras

报  告  人：Ivan Shestakov 院士 (邀请人：张泽锐)

                                      巴西圣保罗大学

时      间： 11月22日  14：30-15:30

地     点：数科院西楼111报告厅

报告人简介:

        Ivan Shestakov是巴西圣保罗大学数学与统计研究所名誉教授。他是巴西科学院院士、发展中国家科学进步世界科学院院士、美国数学学会会员。2007 年，他荣获美国数学学会 E.H.Moore 研究论文奖，2017 年，他荣获索博列夫数学研究所“数学杰出贡献”金质奖章。

摘      要：

       An automorphism φ of a free algebra F_V [x1, . . . , xn] from a class V is called elementary if it is of the form 

φ : (x_1, . . . , x_i , . . . , x_n) \mapsto (x_1, . . . , λx_i + f, . . . , x_n), 

where 0 \neq λ ∈ F and the element f belongs to the subalgebra generated by x_1, . . . , x_{i−1}, x_{i+1} . . . , x_n. 

     An automorphism is called tame if it can be represented as a composition of elementary automorphisms, otherwise it is called wild. 

     It is known that the automorphisms of polynomial algebra and of free associative algebra are tame in case of two generators while in case of three generators there exist wild automorphisms. 

     In our talk, we will discuss known results and open problems on tame and wild automorphisms in various classes of algebras.

        欢迎老师、同学们参加、交流！