Seminars: V. L. Popov, Simple algebras and invariants of linear actions

SEMINARS


Shafarevich Seminar November 18, 2014 15:00, Moscow, Steklov Mathematical Institute, room 540 (Gubkina 8)

Simple algebras and invariants of linear actions V. L. Popov
Abstract: I shall first describe a general construction that yields, for every finite dimensional $G$-module $V$ of a group $G$ admitting a structure of simple (not necessarily associative) algebra $A$ such that $\operatorname{Aut} A=G$, some polynomial $G$-invariant functions on the direct sum of several copies of $V$. I shall then address the following three arising questions: (1) How many functions are obtained in this manner? In particular, do they generate the field of all $G$-invariant rational functions? (2) When does such a structure of simple algebra exists? (3) Which groups arise in this context?