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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?


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