Query：
学者姓名：杨士林
Refining：
Year
Type
Indexed by
Source
Complex
Co-Author
Language
Clean All
Abstract ：
In this paper, we focus on studying two classes of finite dimensional triangle-associative algebras, which are extensions of a family of 2n2 2-dimensional Kac-Paljutkin type semi-simple Hopf algebras H2n2. 2n 2 . All their indecomposable modules are classified. Furthermore, their representation rings are described by generators with suitable relations.
Keyword ：
tensor product tensor product triangle -associative algebra triangle -associative algebra representation ring representation ring
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Su, Dong , Yang, Shilin . Representation rings of extensions of Hopf algebra of Kac-Paljutkin type [J]. | ELECTRONIC RESEARCH ARCHIVE , 2024 , 32 (9) : 5201-5230 . |
| MLA | Su, Dong 等. "Representation rings of extensions of Hopf algebra of Kac-Paljutkin type" . | ELECTRONIC RESEARCH ARCHIVE 32 . 9 (2024) : 5201-5230 . |
| APA | Su, Dong , Yang, Shilin . Representation rings of extensions of Hopf algebra of Kac-Paljutkin type . | ELECTRONIC RESEARCH ARCHIVE , 2024 , 32 (9) , 5201-5230 . |
| Export to | NoteExpress RIS BibTex |
Abstract ：
In this paper, all string modules of one class of basic Hopf algebras of tame type, which are denoted by H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {H}_2$$\end{document} are studied. Firstly, the isomorphism classes of all string modules of H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {H}_2$$\end{document} are classified. Then the projective class ring of H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {H}_2$$\end{document} is described. Finally, the McKay matrix and the corresponding McKay quiver of H2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {H}_2$$\end{document} are discussed.
Keyword ：
McKay matrix McKay matrix String modules String modules Basic Hopf algebra Basic Hopf algebra
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Lin, Shiyu , Yang, Shilin . Representations of Basic Hopf Algebras of Tame Type [J]. | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY , 2024 , 50 (5) . |
| MLA | Lin, Shiyu 等. "Representations of Basic Hopf Algebras of Tame Type" . | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY 50 . 5 (2024) . |
| APA | Lin, Shiyu , Yang, Shilin . Representations of Basic Hopf Algebras of Tame Type . | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY , 2024 , 50 (5) . |
| Export to | NoteExpress RIS BibTex |
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
Cite：
Copy from the list or Export to your reference management。
| 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 . |
| Export to | NoteExpress RIS BibTex |
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
Cite：
Copy from the list or Export to your reference management。
| 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 . |
| Export to | NoteExpress RIS BibTex |
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
Cite：
Copy from the list or Export to your reference management。
| 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 . |
| Export to | NoteExpress RIS BibTex |
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
Cite：
Copy from the list or Export to your reference management。
| 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 . |
| Export to | NoteExpress RIS BibTex |
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
Cite：
Copy from the list or Export to your reference management。
| 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 . |
| Export to | NoteExpress RIS BibTex |
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
Cite：
Copy from the list or Export to your reference management。
| 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) . |
| Export to | NoteExpress RIS BibTex |
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.
Cite：
Copy from the list or Export to your reference management。
| 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 . |
| Export to | NoteExpress RIS BibTex |
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
Cite：
Copy from the list or Export to your reference management。
| 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 . |
| Export to | NoteExpress RIS BibTex |
Export
| Results： |
Selected to |
| Format： |
