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学者姓名：杨士林
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摘要 ：
In this paper, we study the structure of F-q-linear skewcyclic codes over F-q2. Some good F-q-linear skew cyclic codes over F-q2 are constructed. Moreover, as an application, some good quantum codes are obtained by F-q-linear skew cyclic codes over F-q2.
关键词 ：
F-q-Linear skew cyclic codes over F-q2 F-q-Linear skew cyclic codes over F-q2 Trace-alternating form Trace-alternating form Quantum codes Quantum codes
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| GB/T 7714 | Gao, Yun , Gao, Jian , Yang, Shilin et al. F-q-Linear skew cyclic codes over F-q2 and their applications of quantum codes construction [J]. | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING , 2021 . |
| MLA | Gao, Yun et al. "F-q-Linear skew cyclic codes over F-q2 and their applications of quantum codes construction" . | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING (2021) . |
| APA | Gao, Yun , Gao, Jian , Yang, Shilin , Fu, Fang-Wei . F-q-Linear skew cyclic codes over F-q2 and their applications of quantum codes construction . | JOURNAL OF APPLIED MATHEMATICS AND COMPUTING , 2021 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Let F-qt be a finite field of cardinality q(t), where q is a power of a prime number p and t >= 1 is a positive integer. Firstly, a family of cyclic F-q-linear F-qt-codes of length n is given, where n is a positive integer coprime to q. Then according to the structure of this kind of codes, we construct 60 optimal cyclic Fq-linear F-q2-codes which have the same parameters as the MDS codes over F-q2.
关键词 ：
Cyclic F-q-linear F(q)t-codes Cyclic F-q-linear F(q)t-codes MDS codes MDS codes optimal codes optimal codes
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| GB/T 7714 | Gao, Yun , Yang, Shilin , Fu, Fang-Wei . SOME OPTIMAL CYCLIC F-q-LINEAR F-qt-CODES [J]. | ADVANCES IN MATHEMATICS OF COMMUNICATIONS , 2021 , 15 (3) : 387-396 . |
| MLA | Gao, Yun et al. "SOME OPTIMAL CYCLIC F-q-LINEAR F-qt-CODES" . | ADVANCES IN MATHEMATICS OF COMMUNICATIONS 15 . 3 (2021) : 387-396 . |
| APA | Gao, Yun , Yang, Shilin , Fu, Fang-Wei . SOME OPTIMAL CYCLIC F-q-LINEAR F-qt-CODES . | ADVANCES IN MATHEMATICS OF COMMUNICATIONS , 2021 , 15 (3) , 387-396 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In this paper, we construct all the indecomposable modules of a class of non-pointed Hopf algebras, which are quotient Hopf algebras of a class of prime Hopf algebras of GK-dimension one. Then the decomposition formulas of the tensor product of any two indecomposable modules are established. Based on these results, the representation ring of the Hopf algebras is characterized by generators and some relations.
关键词 ：
Hopf algebra Hopf algebra indecomposable module indecomposable module representation ring representation ring representation type representation type tensor product tensor product
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| GB/T 7714 | Yang, Ruifang , Yang, Shilin . Representations of a non-pointed Hopf algebra [J]. | AIMS MATHEMATICS , 2021 , 6 (10) : 10523-10539 . |
| MLA | Yang, Ruifang et al. "Representations of a non-pointed Hopf algebra" . | AIMS MATHEMATICS 6 . 10 (2021) : 10523-10539 . |
| APA | Yang, Ruifang , Yang, Shilin . Representations of a non-pointed Hopf algebra . | AIMS MATHEMATICS , 2021 , 6 (10) , 10523-10539 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
We construct the Grothendieck rings of a class of 2n(2) dimensional semisimple Hopf Algebras H-2n2; which can be viewed as a generalization of the 8 dimensional Kac-Paljutkin Hopf algebra H-8. All irreducible H-2n2-modules are classified. Furthermore, we describe the Grothendieck rings r(H-2n2) by generators and relations explicitly.
关键词 ：
Grothendieck ring Grothendieck ring Hopf algebra Hopf algebra irreducible module irreducible module
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| GB/T 7714 | Chen, Jialei , Yang, Shilin , Wang, Dingguo . Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type [J]. | FRONTIERS OF MATHEMATICS IN CHINA , 2021 , 16 (1) : 29-47 . |
| MLA | Chen, Jialei et al. "Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type" . | FRONTIERS OF MATHEMATICS IN CHINA 16 . 1 (2021) : 29-47 . |
| APA | Chen, Jialei , Yang, Shilin , Wang, Dingguo . Grothendieck rings of a class of Hopf algebras of Kac-Paljutkin type . | FRONTIERS OF MATHEMATICS IN CHINA , 2021 , 16 (1) , 29-47 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Wu-Liu-Ding algebras, that is D(m, d, xi), are a class of non-pointed affine prime regular Hopf algebras of GK-dimension one. In this paper, we mainly study a class of quotient algebras of D(m, d, xi), denoted by D'(m, d, xi), which are 2m(2)d-dimensional non-pointed semisimple Hopf algebras. For a better understanding of the structure of the Hopf algebra D'(m, d, xi), we have considered the Grothendieck rings of D'(m, d, xi) and their Casimir numbers when d is odd in our previous paper. In this paper we continue dealing with the more complex case when d is even. It turns out that the Grothendieck rings of D'(m, d, xi) are generated by four elements subject to some relations. Then we give the Casimir numbers of the Grothendieck rings of D'(1, d, xi) and D'(2, d, xi).
关键词 ：
Frobenius algebra Frobenius algebra Casimir number Casimir number Grothendieck ring Grothendieck ring
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| GB/T 7714 | Yang, Ruifang , Yang, Shilin . The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (II) [J]. | COMMUNICATIONS IN ALGEBRA , 2020 , 49 (5) : 2041-2073 . |
| MLA | Yang, Ruifang et al. "The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (II)" . | COMMUNICATIONS IN ALGEBRA 49 . 5 (2020) : 2041-2073 . |
| APA | Yang, Ruifang , Yang, Shilin . The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (II) . | COMMUNICATIONS IN ALGEBRA , 2020 , 49 (5) , 2041-2073 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
The aim of this paper is to study bialgebras(Hopf algebras) on the skew polynomial algebras R[ z; s] of automorphism type, which comultiplication defined on the variable z is extended by a Drinfeld twist J for a Hopf algebra R. Firstly, we establish some necessary and sufficient conditions that are of Hopf algebra structures on the localization of skew polynomial ring R[z; s] and on the quotients of R[ z; s]/I, for a certain Hopf ideal I of R[ z; s]. Then, we give some examples for these results. Specially, the non-semisimple and non-pointed 16 dimension self-dual Hopf algebra is also constructed by the Ore extensions of automorphism type.
关键词 ：
Drinfeld twist Drinfeld twist Hopf algebra Hopf algebra Ore extension Ore extension Twisted homomorphism Twisted homomorphism
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| GB/T 7714 | Yang, Shilin , Zhang, Yongfeng . Ore Extensions of Automorphism Type for Hopf Algebras [J]. | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY , 2020 , 46 (2) : 487-501 . |
| MLA | Yang, Shilin et al. "Ore Extensions of Automorphism Type for Hopf Algebras" . | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY 46 . 2 (2020) : 487-501 . |
| APA | Yang, Shilin , Zhang, Yongfeng . Ore Extensions of Automorphism Type for Hopf Algebras . | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY , 2020 , 46 (2) , 487-501 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
The aim of this paper is to classify all Hopf algebra structures on the quotient of Ore extensions H-4[z;sigma]of automorphism type for the Sweedler ' s 4-dimensional Hopf algebra H-4. Firstly, we calculate all equivalent classes of twisted homomorphisms (sigma,J) for H-4. Then we give the classification of all bialgebra (Hopf algebra) structures on the quotients of H-4[z;sigma] up to isomorphism.
关键词 ：
Drinfeld twist Drinfeld twist Hopf algebra Hopf algebra Ore extension Ore extension twisted homomorphism twisted homomorphism
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| GB/T 7714 | Yang, Shilin , Zhang, Yongfeng . Ore Extensions for the Sweedler's Hopf Algebra H-4 [J]. | MATHEMATICS , 2020 , 8 (8) . |
| MLA | Yang, Shilin et al. "Ore Extensions for the Sweedler's Hopf Algebra H-4" . | MATHEMATICS 8 . 8 (2020) . |
| APA | Yang, Shilin , Zhang, Yongfeng . Ore Extensions for the Sweedler's Hopf Algebra H-4 . | MATHEMATICS , 2020 , 8 (8) . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Let Q be a finite union of Dynkin quivers, G subset of Aut(kQ) a finite abelian group, (Q) over cap the generalized McKay quiver of (Q, G) and Gamma(Q) the Auslander-Reiten quiver of kQ. Then G acts functorially on the quiver Gamma(Q). We show that the Auslander-Reiten quiver of k (Q) over cap coincides with the generalized McKay quiver of (Gamma(Q), G).
关键词 ：
Auslander-Reiten quiver Auslander-Reiten quiver duality duality generalized McKay quiver generalized McKay quiver
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| GB/T 7714 | Hou, Bo , Yang, Shilin . THE DUALITY OF AUSLANDER-REITEN QUIVER OF PATH ALGEBRAS [J]. | CZECHOSLOVAK MATHEMATICAL JOURNAL , 2019 , 69 (4) : 925-943 . |
| MLA | Hou, Bo et al. "THE DUALITY OF AUSLANDER-REITEN QUIVER OF PATH ALGEBRAS" . | CZECHOSLOVAK MATHEMATICAL JOURNAL 69 . 4 (2019) : 925-943 . |
| APA | Hou, Bo , Yang, Shilin . THE DUALITY OF AUSLANDER-REITEN QUIVER OF PATH ALGEBRAS . | CZECHOSLOVAK MATHEMATICAL JOURNAL , 2019 , 69 (4) , 925-943 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In this paper, we study the representations of a class of small nonstandard quantum group over which the isomorphism classes of all indecomposable modules are classified, and the decomposition formulas of the tensor product of arbitrary indecomposable modules and simple (or projective) modules are established. The projective class rings and Grothendieck rings of are also characterized.
关键词 ：
indecomposable module indecomposable module Nonstandard quantum group Nonstandard quantum group tensor product tensor product
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| GB/T 7714 | Su, Dong , Yang, Shilin . Representations of the small nonstandard quantum groups [J]. | COMMUNICATIONS IN ALGEBRA , 2019 , 47 (12) : 5039-5062 . |
| MLA | Su, Dong et al. "Representations of the small nonstandard quantum groups" . | COMMUNICATIONS IN ALGEBRA 47 . 12 (2019) : 5039-5062 . |
| APA | Su, Dong , Yang, Shilin . Representations of the small nonstandard quantum groups . | COMMUNICATIONS IN ALGEBRA , 2019 , 47 (12) , 5039-5062 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Finite dimensional ribbon Hopf (super) algebras play an important role in constructing invariants of 3-manifolds. In the present paper, the authors give a necessary and sufficient condition for the Drinfel'd double of a finite dimensional Hopf superalgebra to have a ribbon element. The criterion can be seen as a generalization of Kauffman and Radford's result in the non-super situation to the Z(2)-graded situation, however, the derivation of the result in the Z(2)-graded case will be much more complicated.
关键词 ：
Drinfel'd double Drinfel'd double Hopf superalgebras Hopf superalgebras Ribbon element Ribbon element
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| GB/T 7714 | Chen, Jialei , Yang, Shilin . Ribbon Hopf Superalgebras and Drinfel'd Double [J]. | CHINESE ANNALS OF MATHEMATICS SERIES B , 2018 , 39 (6) : 1047-1064 . |
| MLA | Chen, Jialei et al. "Ribbon Hopf Superalgebras and Drinfel'd Double" . | CHINESE ANNALS OF MATHEMATICS SERIES B 39 . 6 (2018) : 1047-1064 . |
| APA | Chen, Jialei , Yang, Shilin . Ribbon Hopf Superalgebras and Drinfel'd Double . | CHINESE ANNALS OF MATHEMATICS SERIES B , 2018 , 39 (6) , 1047-1064 . |
| 导入链接 | NoteExpress RIS BibTex |
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