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学者姓名：杨士林
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Abstract ：
In this paper, representations of the 8m-dimensional non-pointed Hopf algebra H-8m of tame type are studied, where m is even. First, the isomorphism classes of all indecomposable modules of H-8m are classified and the components of Auslander-Reiten quivers are constructed. Second, the tensor products of arbitrary indecomposable modules and simple (or projective) modules are established and the projective class rings and Grothendieck rings of H-8m are characterized.
Keyword ：
projective class ring projective class ring Non-pointed Hopf algebra Non-pointed Hopf algebra bound quiver bound quiver
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| GB/T 7714 | Guo, Yaguo , Yang, Shilin . Representations of an 8m-dimensional non-pointed Hopf algebra of tame type [J]. | JOURNAL OF ALGEBRA AND ITS APPLICATIONS , 2023 . |
| MLA | Guo, Yaguo 等. "Representations of an 8m-dimensional non-pointed Hopf algebra of tame type" . | JOURNAL OF ALGEBRA AND ITS APPLICATIONS (2023) . |
| APA | Guo, Yaguo , Yang, Shilin . Representations of an 8m-dimensional non-pointed Hopf algebra of tame type . | JOURNAL OF ALGEBRA AND ITS APPLICATIONS , 2023 . |
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Abstract ：
In this paper, all simple Yetter-Drinfeld modules and indecomposable projective Yetter-Drinfeld modules over a family of non-pointed 8m-dimension Hopf algebras of tame type with rank two, are construted and classified. The technique is Radford's method of constructing Yetter-Drinfeld modules over a Hopf algebra. Furthermore, the projective class rings of the category of Yetter-Drinfeld modules over this class of Hopf algebras are described explicitly by generators and relations.
Keyword ：
tensor product tensor product the projective class ring the projective class ring Yetter-Drinfeld module Yetter-Drinfeld module simple subcomodule simple subcomodule
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| GB/T 7714 | Guo, Yaguo , Yang, Shilin . Projective class rings of a kind of category of Yetter-Drinfeld modules [J]. | AIMS MATHEMATICS , 2023 , 8 (5) : 10997-11014 . |
| MLA | Guo, Yaguo 等. "Projective class rings of a kind of category of Yetter-Drinfeld modules" . | AIMS MATHEMATICS 8 . 5 (2023) : 10997-11014 . |
| APA | Guo, Yaguo , Yang, Shilin . Projective class rings of a kind of category of Yetter-Drinfeld modules . | AIMS MATHEMATICS , 2023 , 8 (5) , 10997-11014 . |
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Abstract ：
As is well known, a class of 2n(2)-dimensional Kac-Paljutkin Hopf algebras H(2)n(2) was introduced by Pansera. It is the generalization of the 8-dimensional Kac-Paljutkin Hopf algebra H-8. In this paper, the classification of Yetter-Drinfeld modules over H-2n(2) is given by Radford's method of constructing Yetter-Drinfeld modules for a Hopf algebra. Furthermore, the tensor product of Yetter-Drinfeld modules over H-2n(2) is established, and the Grothendieck ring r((2nH2nYD)-H-H-H-2-Y-2) is described explicitly by generators and relations.Communicated by Julia Plavnik
Keyword ：
tensor product tensor product Kac-Paljutkin algebra Kac-Paljutkin algebra Grothendieck ring Grothendieck ring Yetter-Drinfeld module Yetter-Drinfeld module
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| GB/T 7714 | Guo, Yaguo , Yang, Shilin . The Grothendieck ring of Yetter-Drinfeld modules over a class of 2n(2)-dimensional Kac-Paljutkin Hopf algebras [J]. | COMMUNICATIONS IN ALGEBRA , 2023 , 51 (11) : 4517-4566 . |
| MLA | Guo, Yaguo 等. "The Grothendieck ring of Yetter-Drinfeld modules over a class of 2n(2)-dimensional Kac-Paljutkin Hopf algebras" . | COMMUNICATIONS IN ALGEBRA 51 . 11 (2023) : 4517-4566 . |
| APA | Guo, Yaguo , Yang, Shilin . The Grothendieck ring of Yetter-Drinfeld modules over a class of 2n(2)-dimensional Kac-Paljutkin Hopf algebras . | COMMUNICATIONS IN ALGEBRA , 2023 , 51 (11) , 4517-4566 . |
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Abstract ：
Since intuitionistic fuzzy set only deals with uncertainty but not periodicity, therefore to overcome, this situation complex intuitionistic fuzzy set is a better tool that deals with both uncertainty and periodicity. Also, Bonferroni mean operator has the advantage of considering interrelationships between parameters, but it deals with only the crisp data. Recently, to deal with fuzzy data, many extensions of Bonferroni operators have been developed. Motivated by the CIFS and BM operators, in this paper, we proposed some Dombi Bonferroni mean operators to deal with CIF information. Dombi Bonferroni mean operators are special cases of general T-conorm and T-norm, which have the advantage of good flexibility with a general parameter. We proposed the complex intuitionistic fuzzy Dombi Bonferroni mean (CIFDBM) operator, complex intuitionistic fuzzy Dombi weighted Bonferroni mean (CIFDWBM) operator, complex intuitionistic fuzzy Dombi geometric Bonferroni mean (CIFDGBM) operator, and complex intuitionistic fuzzy Dombi weighted geometric Bonferroni mean (CIFDWGBM) operator. Some properties of the developed operators are discussed in detail, and different cases are investigated. Moreover, a multicriteria group decision-making (MCGDM) method is developed based on the proposed aggregation operators. Finally, a numerical example of information security management evaluation is given in order to demonstrate the application and effectiveness of the proposed approach. A comparative study is also conducted in order to show the advantage of the developed method.
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| GB/T 7714 | Azam, Muhammad , Ali Khan, Muhammad Sajjad , Yang, Shilin . A Decision-Making Approach for the Evaluation of Information Security Management under Complex Intuitionistic Fuzzy Set Environment [J]. | JOURNAL OF MATHEMATICS , 2022 , 2022 . |
| MLA | Azam, Muhammad 等. "A Decision-Making Approach for the Evaluation of Information Security Management under Complex Intuitionistic Fuzzy Set Environment" . | JOURNAL OF MATHEMATICS 2022 (2022) . |
| APA | Azam, Muhammad , Ali Khan, Muhammad Sajjad , Yang, Shilin . A Decision-Making Approach for the Evaluation of Information Security Management under Complex Intuitionistic Fuzzy Set Environment . | JOURNAL OF MATHEMATICS , 2022 , 2022 . |
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Abstract ：
Let w(2,2)(s) (s = 0, 1) be two classes of weak Hopf algebras corresponding to the Sweedler Hopf algebra, and r(w(2,2)(s)) be the representation rings of w(2,2)(s). In this paper, we investigate the automorphism groups Aut(r(w)(2,2)(s))) of r(w(2,2)(s)), and discuss some properties of Aut(r(w(2,2)(s))). We obtain that Aut(r(w(2,2)(0))) is isomorphic to K-4, where K-4 is the Klein four-group. It is shown that Aut(r(w(2,2)(1))) is a non-commutative infinite solvable group, but it is not nilpotent. In addition, Aut(r(w(2,2)(1))) is isomorphic to (Z x Z(2)) (sic) Z(2), and its centre is isomorphic to Z(2).
Keyword ：
representation ring representation ring weak Hopf algebra weak Hopf algebra Sweedler Hopf algebra Sweedler Hopf algebra automorphism group automorphism group
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| GB/T 7714 | Su, Dong , Yang, Shilin . Automorphism groups of representation rings of the weak Sweedler Hopf algebras [J]. | AIMS MATHEMATICS , 2022 , 7 (2) : 2318-2330 . |
| MLA | Su, Dong 等. "Automorphism groups of representation rings of the weak Sweedler Hopf algebras" . | AIMS MATHEMATICS 7 . 2 (2022) : 2318-2330 . |
| APA | Su, Dong , Yang, Shilin . Automorphism groups of representation rings of the weak Sweedler Hopf algebras . | AIMS MATHEMATICS , 2022 , 7 (2) , 2318-2330 . |
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Abstract ：
Wu-Liu-Ding algebras are a class of affine prime regular Hopf algebras of GK-dimension one, denoted by D(m,d,xi). In this paper, we consider their quotient algebras D '(m,d,xi), which are a new class of non-pointed semisimple Hopf algebras. We describe the Grothendieck rings of D '(m,d,xi) when d is odd. It turns out that the Grothendieck rings are commutative rings generated by three elements subject to some relations. Then we compute the Casimir numbers of the Grothendieck rings for m = 1 and m = 3.
Keyword ：
Frobenius algebra Frobenius algebra Grothendieck ring Grothendieck ring Casimir number Casimir number
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| GB/T 7714 | Yang, Ruifang , Yang, Shilin . The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (I) [J]. | JOURNAL OF ALGEBRA AND ITS APPLICATIONS , 2022 , 21 (09) . |
| MLA | Yang, Ruifang 等. "The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (I)" . | JOURNAL OF ALGEBRA AND ITS APPLICATIONS 21 . 09 (2022) . |
| APA | Yang, Ruifang , Yang, Shilin . The Grothendieck rings of Wu-Liu-Ding algebras and their Casimir numbers (I) . | JOURNAL OF ALGEBRA AND ITS APPLICATIONS , 2022 , 21 (09) . |
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Abstract ：
We first describe the Sekine quantum groups A(k) (the finite-dimensional Kac algebra of Kac-Paljutkin type) by generators and relations explicitly, which maybe convenient for further study. Then we classify all irreducible representations of A(k) and describe their representation rings r(A(k)). Finally, we compute the the Frobenius-Perron dimension of the Casimir element and the Casimir number of r(A(k)).
Keyword ：
representation ring representation ring Sekine quantum group Sekine quantum group Casimir number Casimir number
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| GB/T 7714 | Chen, Jialei , Yang, Shilin . REMARKS ON SEKINE QUANTUM GROUPS [J]. | CZECHOSLOVAK MATHEMATICAL JOURNAL , 2022 , 72 (3) : 695-707 . |
| MLA | Chen, Jialei 等. "REMARKS ON SEKINE QUANTUM GROUPS" . | CZECHOSLOVAK MATHEMATICAL JOURNAL 72 . 3 (2022) : 695-707 . |
| APA | Chen, Jialei , Yang, Shilin . REMARKS ON SEKINE QUANTUM GROUPS . | CZECHOSLOVAK MATHEMATICAL JOURNAL , 2022 , 72 (3) , 695-707 . |
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Abstract ：
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.
Keyword ：
Cyclic F-q-linear F(q)t-codes Cyclic F-q-linear F(q)t-codes optimal codes optimal codes MDS codes MDS 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 等. "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 . |
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Abstract ：
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.
Keyword ：
irreducible module irreducible module Grothendieck ring Grothendieck ring Hopf algebra Hopf algebra
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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 等. "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 . |
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Abstract ：
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.
Keyword ：
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 , 68 (1) : 349-361 . |
| 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 68 . 1 (2021) : 349-361 . |
| 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 , 68 (1) , 349-361 . |
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