仿射格拉斯曼的等变定向同调

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2024-10-02 DOI:10.1016/j.jalgebra.2024.09.009

Changlong Zhong

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引用次数: 0

摘要

我们将仿射格拉斯曼的小副边等变 K-同调性质推广到莱文和莫雷尔意义上的一般定向（共）同调理论。我们使用的主要工具是与仿射根系统相关联的形式仿射 Demazure 代数。更准确地说，我们证明仿射格拉斯曼的小副等变定向同调满足戈尔斯基-科特维茨-麦克弗森（GKM）条件。我们还证明了它的对偶，即小副边等变同调，与形式仿射 Demazure 代数中点的等变定向同调的中心化同构。

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Equivariant oriented homology of the affine Grassmannian

We generalize the property of small-torus equivariant K-homology of the affine Grassmannian to general oriented (co)homology theory in the sense of Levine and Morel. The main tool we use is the formal affine Demazure algebra associated to the affine root system. More precisely, we prove that the small-torus equivariant oriented cohomology of the affine Grassmannian satisfies the Goresky-Kottwitz-MacPherson (GKM) condition. We also show that its dual, the small-torus equivariant homology, is isomorphic to the centralizer of the equivariant oriented cohomology of a point in the formal affine Demazure algebra.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.