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Enveloping algebras of Slodowy slices and the Joseph ideal

Alexander Premet — 2007

Journal of the European Mathematical Society

Let G be a simple algebraic group over an algebraically closed field 𝕜 of characteristic 0, and 𝔤 = Lie G . Let ( e , h , f ) be an 𝔰 𝔩 2 -triple in 𝔤 with e being a long root vector in 𝔤 . Let ( · , · ) be the G -invariant bilinear form on 𝔤 with ( e , f ) = 1 and let χ 𝔤 * be such that χ ( x ) = ( e , x ) for all x 𝔤 . Let 𝒮 be the Slodowy slice at e through the adjoint orbit of e and let H be the enveloping algebra of 𝒮 ; see [31]. In this article we give an explicit presentation of H by generators and relations. As a consequence we deduce that H contains an ideal...

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