

Seminar of the Department of Algebra and of the Department of Algebraic Geometry (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^{} 
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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?

