摘要翻译：
设g是特征P>0的代数闭域k上连通还原群g的李代数。设$Z$是g的泛包络代数u=u(g)的中心。它的最大谱称为G的Zassenhaus变型。我们证明了在G上某些温和的假设下，Z的分式场Frac(Z)与具有扭曲G-作用的对偶空间G*的函数场是G-等变同构的。特别地，Frac(Z)是有理的。这证实了J.Alev的一个猜想。进一步证明了Z是唯一的因子分解域，证实了a.Braun和C.Hajarnavis的一个猜想。最近，a.Premet利用Colliot-Thelene、Kunyavskii、Popov和Reichstein的结果和约化mod p变元，证明了Gelfand-Kirillov猜想对于非a型、C型或G2型的简单复李代数不能成立。
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英文标题：
《The Zassenhaus variety of a reductive Lie algebra in positive
  characteristic》
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作者：
Rudolf Tange
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最新提交年份：
2009
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分类信息：

一级分类：Mathematics        数学
二级分类：Rings and Algebras        环与代数
分类描述：Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups
非交换环与代数，非结合代数，泛代数与格论，线性代数，半群
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  Let g be the Lie algebra of a connected reductive group G over an algebraically closed field k of characteristic p>0. Let $Z$ be the centre of the universal enveloping algebra U=U(g) of g. Its maximal spectrum is called the Zassenhaus variety of g. We show that, under certain mild assumptions on G, the field of fractions Frac(Z) of Z is G-equivariantly isomorphic to the function field of the dual space g* with twisted G-action. In particular Frac(Z) is rational. This confirms a conjecture J. Alev. Furthermore we show that Z is a unique factorisation domain, confirming a conjecture of A. Braun and C. Hajarnavis. Recently, A. Premet used the above result about Frac(Z), a result of Colliot-Thelene, Kunyavskii, Popov and Reichstein and reduction mod p arguments to show that the Gelfand-Kirillov conjecture cannot hold for simple complex Lie algebras that are not of type A, C or G_2.
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PDF链接：
https://arxiv.org/pdf/0811.4568