Abstract:

 

Symmetric functions, or in broader generality invariant functions, is a classical topic since Newton. In 1916, Noether proved a theorem that the ring of invariant polynomials is finitely generated, hence raised the Noether's problem on whether the field of invariant rational functions is purely transcendental. Recently, a series of paper studied the topic in the context of noncommutative functions. Precisely, for invariant noncommutative functions, the Noether's theorem on finitely generated is no longer true for all kinds of invariant, but surprisingly Noether problem remains true for certain finite groups.

 

In this talk, we summarize the previous results and introduce our work on the invariant functions under certain infinite group actions.

 

Host: Alan Chang