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学者姓名：唐丽丹
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Abstract ：
通过范畴的两个乘法系定义了右分式的一个等价关系,由此引入以原范畴对象为对象,右分式等价类为态射的范畴的广义局部化概念.最后证明加法范畴的广义局部化范畴仍然是加法范畴.
Keyword ：
乘法系 乘法系 加法范畴 加法范畴 广义局部化 广义局部化
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| GB/T 7714 | 唐丽丹 , 沈臻 . 范畴的广义局部化 [J]. | 福州大学学报（自然科学版） , 2020 , 48 (1) : 1-6 . |
| MLA | 唐丽丹 等. "范畴的广义局部化" . | 福州大学学报（自然科学版） 48 . 1 (2020) : 1-6 . |
| APA | 唐丽丹 , 沈臻 . 范畴的广义局部化 . | 福州大学学报（自然科学版） , 2020 , 48 (1) , 1-6 . |
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Abstract ：
A ray pattern matrix is a matrix whose nonzero entries are all unimodular. An n x n ray pattern matrix A is said to require the weak Perron-Frobenius property if for any n x n entrywise positive matrix K, the spectral radius rho(K circle A) is one of the eigenvalues of K circle A; to require the strong Perron-Frobenius property if rho(K circle A) is an algebraically simple eigenvalue of K circle A and the left and right eigenvectors associated to rho(K circle A) are strictly nonzero. In this paper, necessary and sufficient conditions for ray pattern matrices requiring the weak/strong Perron-Frobenius property are given. (C) 2019 Elsevier Inc. All rights reserved.
Keyword ：
Diagonally similar Diagonally similar Positive cycle Positive cycle Ray pattern Ray pattern Weak/strong Perron-Frobenius property Weak/strong Perron-Frobenius property
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| GB/T 7714 | Liu, Yue , Tang, Lidan . Ray pattern matrices requiring Perron-Frobenius properties [J]. | LINEAR ALGEBRA AND ITS APPLICATIONS , 2019 , 571 : 103-109 . |
| MLA | Liu, Yue 等. "Ray pattern matrices requiring Perron-Frobenius properties" . | LINEAR ALGEBRA AND ITS APPLICATIONS 571 (2019) : 103-109 . |
| APA | Liu, Yue , Tang, Lidan . Ray pattern matrices requiring Perron-Frobenius properties . | LINEAR ALGEBRA AND ITS APPLICATIONS , 2019 , 571 , 103-109 . |
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Abstract ：
We first prove that the subcategory of fixed points of mutation determined by an exceptional object E in a triangulated category coincide with the perpendicular category of E. Based on this characterisation, we prove that the subcategory of fixed points of mutation in the derived category of the coherent sheaves on weighted projective line with genus one is equivalent to the derived category of a hereditary algebra. Meanwhile, we induce two new recollements by left and right mutations from a given recollement.
Keyword ：
exceptional object exceptional object recollement recollement Subcategory of fixed points Subcategory of fixed points
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| GB/T 7714 | Tang, Li Dan . Subcategories of Fixed Points of Mutations by Exceptional Objects in Triangulated Categories [J]. | ACTA MATHEMATICA SINICA-ENGLISH SERIES , 2016 , 32 (2) : 187-198 . |
| MLA | Tang, Li Dan . "Subcategories of Fixed Points of Mutations by Exceptional Objects in Triangulated Categories" . | ACTA MATHEMATICA SINICA-ENGLISH SERIES 32 . 2 (2016) : 187-198 . |
| APA | Tang, Li Dan . Subcategories of Fixed Points of Mutations by Exceptional Objects in Triangulated Categories . | ACTA MATHEMATICA SINICA-ENGLISH SERIES , 2016 , 32 (2) , 187-198 . |
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Abstract ：
首先给出了加法范畴的Abel化与幂等完备化的关系，证明了加法范畴的幂等完备化范畴是其Abel化范畴的投射子范畴；在此基础上，证明了三角范畴recollement的Abel化是Abel范畴的右recollement。
Keyword ：
Abel化 Abel化 recollement recollement 三角范畴 三角范畴
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| GB/T 7714 | 唐丽丹 , 陈清华 . 三角范畴的Recollement与Abel化 [J]. | 莆田学院学报 , 2012 , 19 (5) : 1-4,13 . |
| MLA | 唐丽丹 等. "三角范畴的Recollement与Abel化" . | 莆田学院学报 19 . 5 (2012) : 1-4,13 . |
| APA | 唐丽丹 , 陈清华 . 三角范畴的Recollement与Abel化 . | 莆田学院学报 , 2012 , 19 (5) , 1-4,13 . |
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给出三角范畴recollement中三个三角范畴的维数的关系.在此基础上,通过遗传代数导出范畴的例子说明上述关系式的界均可取到.
Keyword ：
recollement recollement 三角范畴 三角范畴 维数 维数
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| GB/T 7714 | 唐丽丹 , 陈清华 . Recollement中三角范畴的维数 [J]. | 福州大学学报（自然科学版） , 2012 , 40 (6) : 704-706,712 . |
| MLA | 唐丽丹 等. "Recollement中三角范畴的维数" . | 福州大学学报（自然科学版） 40 . 6 (2012) : 704-706,712 . |
| APA | 唐丽丹 , 陈清华 . Recollement中三角范畴的维数 . | 福州大学学报（自然科学版） , 2012 , 40 (6) , 704-706,712 . |
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Abstract ：
给定加法范畴A证明了若A存在右(左)Serre函子,则其幂等完备化范畴A存在右(左)Serre函子.在此基础上,说明了对三角范畴上的recollement D′→D→D″,若D存在Serre函子,则D允许两个关于D″及D′''的反射recollements.作为应用,证明了给定recollement两端三角范畴D′,D″上的t-结构可诱导出中间范畴的幂等完备化范畴D上3个t-结构.
Keyword ：
recollement recollement Serre函子 Serre函子 t-结构 t-结构 反射recollement 反射recollement 幂等完备化 幂等完备化
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| GB/T 7714 | 唐丽丹 . 幂等完备化,Serre函子与Recollement [J]. | 厦门大学学报（自然科学版） , 2011 , 50 (4) : 661-664 . |
| MLA | 唐丽丹 . "幂等完备化,Serre函子与Recollement" . | 厦门大学学报（自然科学版） 50 . 4 (2011) : 661-664 . |
| APA | 唐丽丹 . 幂等完备化,Serre函子与Recollement . | 厦门大学学报（自然科学版） , 2011 , 50 (4) , 661-664 . |
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For any n a (c) 3/4 3, let R(n) denote the root category of finite-dimensional nilpotent representations of cyclic quiver with n vertices. In the present paper, we prove that R(n - 1) is triangle-equivalent to the subcategory of fixed points of certain left (or right) mutation in R(n). As an application, it is shown that the affine Kac-Moody algebra of type A integral (n-2) is isomorphic to a Lie subalgebra of the Kac-Moody algebra of type A integral (n-1).
Keyword ：
Lie algebra Lie algebra root category root category subcategory of fixed points subcategory of fixed points
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| GB/T 7714 | Lin YaNan , Tang LiDan . Subcategories of fixed points of mutations in root categories with type A integral (n-1) [J]. | SCIENCE CHINA-MATHEMATICS , 2010 , 53 (12) : 3057-3066 . |
| MLA | Lin YaNan 等. "Subcategories of fixed points of mutations in root categories with type A integral (n-1)" . | SCIENCE CHINA-MATHEMATICS 53 . 12 (2010) : 3057-3066 . |
| APA | Lin YaNan , Tang LiDan . Subcategories of fixed points of mutations in root categories with type A integral (n-1) . | SCIENCE CHINA-MATHEMATICS , 2010 , 53 (12) , 3057-3066 . |
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