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