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- W2953373087 abstract "The quadratic Poisson Gel'fand-Kirillov problem asks whether the field of fractions of a Poisson algebra is Poisson birationally equivalent to a Poisson affine space, i.e. to a polynomial algebra $K[X_1,..., X_n]$ with Poisson bracket defined by ${X_i,X_j}=lambda_{ij} X_iX_j$ for some skew-symmetric matrix $(lambda_{ij}) in M_n(K)$. This problem was studied in cite{GL} over a field of characteristic 0 by using a Poisson version of the deleting-derivations algorithm of Cauchon. In this paper, we study the quadratic Poisson Gel'fand-Kirillov problem over a field of arbitrary characteristic. In particular, we prove that the quadratic Poisson Gel'fand-Kirillov problem is satisfied for a large class of Poisson algebras arising as semiclassical limits of quantised coordinate rings. For, we introduce the concept of {it higher Poisson derivation} which allows us to extend the Poisson version of the deleting-derivations algorithm from the characteristic 0 case to the case of arbitrary characteristic. When a torus is acting rationally by Poisson automorphisms on a Poisson polynomial algebra arising as the semiclassical limit of a quantised coordinate ring, we prove (under some technical assumptions) that quotients by Poisson prime torus-invariant ideals also satisfy the quadratic Poisson Gel'fand-Kirillov problem. In particular, we show that coordinate rings of determinantal varieties satisfy the quadratic Poisson Gel'fand-Kirillov problem." @default.
- W2953373087 created "2019-06-27" @default.
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- W2953373087 date "2013-02-08" @default.
- W2953373087 modified "2023-09-27" @default.
- W2953373087 title "A quadratic Poisson Gel'fand-Kirillov problem in prime characteristic" @default.
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