Strata of prime ideals of De Concini-Kac-Procesi algebras and Poisson geometry
Strata of prime ideals of De Concini-Kac-Procesi algebras and Poisson geometry
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De Concini-Kac-Procesi 代数和泊松几何的素理想层
DOI：
10.1090/conm/562/11141
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
M. Yakimov
中科院分区：
文献类型：
--
作者：
M. Yakimov
对于每个单李代数g和相应Weyl群De Concini的元素w，Kac和Procesi关联了量子化泛包络代数U_q（g）的子代数U^w_-，它是泛包络代数U（n_- \cap w（n_+））的变形和对应于w的Schubert胞腔的坐标环的量子化。这些代数的环面不变素理想由M\'eriaux和Cauchon [25]以及作者[30]进行了分类。这些理想在[30]中也有明确的描述。他们将U^w_-谱分层的古德尔-莱茨特地层标为环面。在本文中，我们得到了这些层的维数和有理Casimir场对任何开Richardson簇关于标准Poisson结构的超越度的公式[15]。
To each simple Lie algebra g and an element w of the corresponding Weyl group De Concini, Kac and Procesi associated a subalgebra U^w_- of the quantized universal enveloping algebra U_q(g), which is a deformation of the universal enveloping algebra U(n_- \cap w(n_+)) and a quantization of the coordinate ring of the Schubert cell corresponding to w. The torus invariant prime ideals of these algebras were classified by M\'eriaux and Cauchon [25], and the author [30]. These ideals were also explicitly described in [30]. They index the the Goodearl-Letzter strata of the stratification of the spectra of U^w_- into tori. In this paper we derive a formula for the dimensions of these strata and the transcendence degree of the field of rational Casimirs on any open Richardson variety with respect to the standard Poisson structure [15].
量子舒伯特细胞中的原始理想：层的维度
影响因子：
0.8
作者：
Bell J
通讯作者：
Bell J