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学者姓名：陈清花
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Abstract ：
In the present paper, we investigate the universal PBW basis and HN system for the derived Hall algebra of a triangulated category satisfying some finiteness conditions. Furthermore, we study the related stability conditions on the module category A of the path algebra A of an acyclic quiver and on the bounded derived category of A. Moreover, we investigate the relation between the Ringel-Hall algebra and the HN system of A defined by Reineke.
Keyword ：
Derived Hall algebra Derived Hall algebra HN system HN system stability condition stability condition
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| GB/T 7714 | Wang, Xintian , Chen, Qinghua . Stability conditions and derived Hall algebras [J]. | COMMUNICATIONS IN ALGEBRA , 2023 , 51 (8) : 3464-3480 . |
| MLA | Wang, Xintian 等. "Stability conditions and derived Hall algebras" . | COMMUNICATIONS IN ALGEBRA 51 . 8 (2023) : 3464-3480 . |
| APA | Wang, Xintian , Chen, Qinghua . Stability conditions and derived Hall algebras . | COMMUNICATIONS IN ALGEBRA , 2023 , 51 (8) , 3464-3480 . |
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Abstract ：
Let l be an extriangulated category with a proper class xi of E-triangles. We introduce the notions of left Frobenius pairs, left (n-)cotorsion pairs and left (weak) Auslander-Buchweitz contexts with respect to xi in l. We show how to construct left cotorsion pais from left n-cotorsion pairs, and establish a one-to-one correspondence between left Frobenius pairs and left (weak) Auslander-Buchweitz contexts. We also study the relation between a certain class of cotorsion pairs and that of n-cotorsion pairs. These work generalize Ma-Zhao-Huang's results in triangulated categories and partially generalize Becerril-Mendoza-Perez-Santiago's results in abelian categories.
Keyword ：
A proper class of E-triangles A proper class of E-triangles Extriangulated categories Extriangulated categories left Frobenius pairs left Frobenius pairs left n-cotorsion pairs left n-cotorsion pairs left (weak) Auslander-Buchweitz contexts left (weak) Auslander-Buchweitz contexts
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| GB/T 7714 | Tan, Lingling , Gao, Yuqiong , Chen, Qinghua . One-sided Frobenius pairs in extriangulated categories [J]. | COMMUNICATIONS IN ALGEBRA , 2022 , 50 (12) : 5345-5370 . |
| MLA | Tan, Lingling 等. "One-sided Frobenius pairs in extriangulated categories" . | COMMUNICATIONS IN ALGEBRA 50 . 12 (2022) : 5345-5370 . |
| APA | Tan, Lingling , Gao, Yuqiong , Chen, Qinghua . One-sided Frobenius pairs in extriangulated categories . | COMMUNICATIONS IN ALGEBRA , 2022 , 50 (12) , 5345-5370 . |
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Abstract ：
This paper presents an explicit construction of almost split sequences in the category C-m(p) of m-cyclic complexes of projective modules over a finite dimensional hereditary algebra. The proof is different from that in [18] for m = 1.
Keyword ：
Almost split sequence Almost split sequence Cyclic complex Cyclic complex Hereditary algebra Hereditary algebra
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| GB/T 7714 | Chen, Qinghua . Almost split sequences of m-cyclic complexes [J]. | ARCHIV DER MATHEMATIK , 2022 , 119 (6) : 569-581 . |
| MLA | Chen, Qinghua . "Almost split sequences of m-cyclic complexes" . | ARCHIV DER MATHEMATIK 119 . 6 (2022) : 569-581 . |
| APA | Chen, Qinghua . Almost split sequences of m-cyclic complexes . | ARCHIV DER MATHEMATIK , 2022 , 119 (6) , 569-581 . |
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Abstract ：
Let Q be a quiver of type (A) over tilde (n). Let alpha = alpha(1)+alpha(2)+...+alpha(s) be the canonical decomposition. For the polynomials M-Q(alpha, q) that count the number of isoclasses of representations of Q over F-q with dimension vector alpha , we obtain a precise relation between the degree of M-Q(alpha, q) and that of Pi M-s(i=1)Q(alpha(i),q) for an arbitrary dimension vector alpha .
Keyword ：
canonical decomposition canonical decomposition dimension vector dimension vector quiver representation quiver representation
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| GB/T 7714 | Chen, Qinghua , Liu, Ye . CANONICAL DECOMPOSITION AND QUIVER REPRESENTATIONS OF TYPE (A)over-tilde(n) OVER FINITE FIELDS [J]. | BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY , 2022 , 107 (2) : 250-260 . |
| MLA | Chen, Qinghua 等. "CANONICAL DECOMPOSITION AND QUIVER REPRESENTATIONS OF TYPE (A)over-tilde(n) OVER FINITE FIELDS" . | BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 107 . 2 (2022) : 250-260 . |
| APA | Chen, Qinghua , Liu, Ye . CANONICAL DECOMPOSITION AND QUIVER REPRESENTATIONS OF TYPE (A)over-tilde(n) OVER FINITE FIELDS . | BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY , 2022 , 107 (2) , 250-260 . |
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Abstract ：
In this paper we study the category Cm(P) of m-cyclic complexes over P, where P is the category of projective modules over a finite dimensional hereditary algebra A, and describe almost split sequences in Cm(P). This is applied to prove the existence of Hall polynomials in Cm(P) when A is representation finite and m≠. 1. We further introduce the Hall algebra of Cm(P) and its localization in the sense of Bridgeland. In the case when A is representation finite, we use Hall polynomials to define the generic Bridgeland-Hall algebra of A and show that it contains a subalgebra isomorphic to the integral form of the corresponding quantum enveloping algebra. This provides a construction of the simple Lie algebra associated with A. © 2015 Elsevier Inc.
Keyword ：
Cyclic complex; Hall polynomial; Quantum group; Simple Lie algebra Cyclic complex; Hall polynomial; Quantum group; Simple Lie algebra
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| GB/T 7714 | Chen, Q. , Deng, B. . Cyclic complexes, Hall polynomials and simple Lie algebras [J]. | Journal of Algebra , 2015 , 440 : 1-32 . |
| MLA | Chen, Q. 等. "Cyclic complexes, Hall polynomials and simple Lie algebras" . | Journal of Algebra 440 (2015) : 1-32 . |
| APA | Chen, Q. , Deng, B. . Cyclic complexes, Hall polynomials and simple Lie algebras . | Journal of Algebra , 2015 , 440 , 1-32 . |
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