Prime Spectra of Abelian 2-Categories and Categorifications of Richardson Varieties
Prime Spectra of Abelian 2-Categories and Categorifications of Richardson Varieties
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阿贝尔2-范畴的素谱和理查森簇的分类
DOI：
10.1007/978-3-030-23531-4_14
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
M. Yakimov
中科院分区：
文献类型：
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作者：
Kent B. Vashaw;M. Yakimov
我们给出了交换2-范畴的素理想、完全素理想、半素理想和本原理想的一般框架。这提供了张量三角范畴的Balmer素谱的一个非对易版本。这些概念是基于关于交换范畴的厚子范畴和交换2-范畴的稠密理想的包含条件。我们证明了非对易素谱的主要性质的范畴类比。从交换范畴的Serre子范畴和交换2-范畴的Serre理想出发，发展了类似的概念。它们与(\mathbb{Z}_+)-环的Serre素谱有关。作为应用，我们构造了对称Kac-Moody群的开Richardson簇的量子化坐标环范畴，构造了KLR代数模范畴的Serre完全素理想，并求出了它们的Serre商。
We describe a general framework for prime, completely prime, semiprime, and primitive ideals of an abelian 2-category. This provides a noncommutative version of Balmer’s prime spectrum of a tensor triangulated category. These notions are based on containment conditions in terms of thick subcategories of an abelian category and thick ideals of an abelian 2-category. We prove categorical analogs of the main properties of noncommutative prime spectra. Similar notions, starting with Serre subcategories of an abelian category and Serre ideals of an abelian 2-category, are developed. They are linked to Serre prime spectra of \(\mathbb {Z}_+\)-rings. As an application, we construct a categorification of the quantized coordinate rings of open Richardson varieties for symmetric Kac–Moody groups, by constructing Serre completely prime ideals of monoidal categories of modules of the KLR algebras, and by taking Serre quotients with respect to them.
影响因子：
2.5
作者：
K. Goodearl;M. Yakimov
通讯作者：
K. Goodearl;M. Yakimov
量子舒伯特细胞代数和量子理查森簇簇的素因数
DOI：
10.1515/crelle-2016-0046
发表时间：
2019
期刊：
Journal für die reine und angewandte Mathematik (Crelles Journal)
影响因子：
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作者：
Lenagan T
通讯作者：
Lenagan T