Finite W-algebras are relatively new algebras arising in Lie theory and closely related to universal enveloping algebras of semisimple Lie algebras. They originate to Kostant's work of late 70's and were extensively studied during the last decade (Brundan, Ginzburg, Goodwin, Kleshchev, Premet, the speaker and others). In my lecture I will explain how Deformation quantization can be used to define and study these algebras.

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