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Семинар НУЛ АГП "The fourteenth Hilbert problem"

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Доклад Юлии Зайцевой на семинаре лаборатории алгебраических групп преобразований.

The 14th Hilbert problem is formulated as follows: is the algebra of polynomials in n variables, invariant under a subgroup G of GL(n), finitely generated? In 1958, Masayoshi Nagata presented his famous counterexample to this problem. However, at this moment, there is no complete description of the groups G for which the answer is affirmative; there are only a few constructions for counterexamples. We will survey various positive and negative results in this area.