Tame and Wild Automorphisms of Free Algebras
Wednesday, June 1, 7-8 p.m.
By Ivan Shestakov (University of Sao Paulo)
The notion of automorphism captures the idea of symmetry in mathematics. More precisely, an automorphism of an object is an invertible transformation that preserves the object’s structure. Many important objects in algebra possess natural examples of such transformations, which are referred to as elementary automorphisms. For such an object, 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 variables while in case of three variables there exist wild automorphisms. The existence of wild automorphisms was the longstanding Nagata Conjecture, for the resolution of which Ivan Shestakov, together with his co-author Ualbai Umirbaev, was awarded the E. H. Moore Prize by the American Mathematical Society in 2007.
In this talk, Professor Shestakov will discuss known results and open problems on tame and wild automorphisms in various classes of algebras.
Presented by Atlantic Algebra Centre