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International conference "Algebra and Mathematical Logic" dedicated to the 100-th birthday of Professor V. V. Morozov
September 27, 2011 11:20, Kazan
 


Invariant rational functions on semisimple Lie algebras and the Gelfand–Kirillov conjecture

V. L. Popov

Steklov Mathematical Institute, Russian Academy of Sciences

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Abstract: The talk focuses on the recent solution (by J.-L. Colliot-Thélène, B. Kunyavskii, V. L. Popov, and Z. Reichstein) of the rationality problem of the fields of rational functions on semisimple Lie algebras and on the heavily based on this solution constructing (by A. Premet) counterexamples to the Gelfand–Kirillov conjecture on the fields of fractions of the universal enveloping algebras of simple Lie algebras.

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