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Fan Kong

Publications and source records attributed to Fan Kong.

6 recordsLinked to original sources
arXiv2026

The cyclotomic non-degenerate Hecke algebras of arbitrary Weyl groups

We construct Khovanov--Lauda--Rouquier-like generators for certain modified forms of non-degenerate affine Hecke algebras associated with arbitrary Weyl groups after localization. These generators yield non-graded KLR-like presentations of the modified algebras. As an application, we establish isomorphisms between direct sums of blocks of cyclotomic Hecke algebras of arbitrary Weyl groups and cyclotomic quotients of the resulting non-graded KLR-like algebras. We also explain how these isomorphisms identify the generalized weight-space decomposition of cyclotomic Hecke modules with the idempotent decomposition of modules over the KLR-like presentation.

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arXiv2021

The Brundan-Kleshchev isomorphism revisited

We give a short and unified proof of the Brundan-Kleshchev isomorphism between blocks of cyclotomic Hecke algebras and cyclotomic KhovanovLauda-Rouquier algebras of type A.

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arXiv2014

From CM-finite to CM-free

The aim of this paper is twofold. On one hand, we prove a slight generalization of the stability for Gorenstein categories in [SWSW] and [Huang]; and show that the relative Auslander algebra of a CM-finite algebra is CM-free. On the other hand, we describe the bounded derived category, and the Gorenstein defect category introduced in [BJO], via Gorenstein-projective objects; and we show that the Gorenstein defect category of a CM-finite algebra is triangle-equivalent to the singularity category of its relative Auslander algebra.

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arXiv2012

Generalization of the Correspondence about DTr-selfinjective algebras

We give a correspondence between (n-1)-DTr-selfinjective algebras and algebras with dominant dimension and selinjective dimension being both n for any n bigger than 1 . Furthermore, we show the relation between the module categories of the two kinds of algebras. At last we show the sepcial condition n = 2.

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arXiv2012

Decomposition of torsion pairs on module categories

In this article, we generalize the concept of torsion pairs and study its structure. As a trial of obtaining all torsion pairs, we decompose torsion pairs by projective modules and injective modules. Then we calculate torsion pairs on the algebra KAn and tub categories. At last we try to find all torsion pairs on the module categories of finite dimensional hereditary algebras.

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