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THE UNIVERSAL DUAL COMODULE OF MODULE IN HOPF ALGEBRAS 被引量:1
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作者 郝志峰 冯良贵 《Acta Mathematica Scientia》 SCIE CSCD 2003年第3期289-296,共8页
The purpose of this paper is to present some dual properties of dual comodule. It turns out that dual comodule has universal property (cf.Theorem 2). Since (( )*,()°) is an adjoint pair (cf.Theorem 3), some nice ... The purpose of this paper is to present some dual properties of dual comodule. It turns out that dual comodule has universal property (cf.Theorem 2). Since (( )*,()°) is an adjoint pair (cf.Theorem 3), some nice properties of functor ( )° are obtained. Finally Theoram 4 provides that the cotensor product is the dual of the tensor product by (M (?)A N)°≌M°□A°N°. Moreover, the result Hom(M,JV)≌ComA°(N°,M°) is proved for finite related modules M, N over a reflexive algebra A. 展开更多
关键词 Universal dual comodule hopf algebras cotensor product adjoint pair
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QUANTUM COMODULE APPROACH THE SOLUTION OF THE QUANTUM YANG-BAXTER EQUATION
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作者 李立斌 李尚志 《Acta Mathematica Scientia》 SCIE CSCD 2000年第2期206-212,共7页
In this paper, the relationship between solutions of the Quantum Yang-Baxter Equation and quantum comodules, and some properties of the quantum comodule category are characterized here. These results make it possible ... In this paper, the relationship between solutions of the Quantum Yang-Baxter Equation and quantum comodules, and some properties of the quantum comodule category are characterized here. These results make it possible to give some set-theoretical solutions of the Quantum Yang-Baxter Equation. 展开更多
关键词 Quantum Yang-Baxter Equation quantum comodule SOLUTION hopf algebra
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由弱H-Hopf模代数构造Rota-Baxter代数
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作者 刘琳琳 《河南工学院学报》 CAS 2024年第1期35-37,共3页
给出弱H-Hopf模代数的定义及其构造定理,进而由弱H-Hopf模代数出发构造Rota-Baxter代数并提供具体的例子。
关键词 Rota-Baxter代数 hOPF代数 h-hopf模代数
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A Maschke Type Theorem for Weak Hopf π-Comodules
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作者 贾玲 陈笑缘 《Chinese Quarterly Journal of Mathematics》 2015年第1期144-152,共9页
In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introd... In this paper, we mainly generalize a Maschke type theorem to the setting of a weak Hopf group coalgebra. First we introduce the notion of a weak Hopf group coalgebra as a generalization of Hopf group coalgebra introduced in [7] and a weak Hopf algebra introduced in [2]. And we study some basic properties of weak Hopf group coalgebras. Next we aim at finding some sucient conditions under which an epimorphism of weak (H, A) Hopf π-comodule splits if it splits as an A-module morphism and give an application of our results. 展开更多
关键词 weak hopf π-coalgebra weak(h A) hopf π-comodules Maschke type theorem
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Fuzzy dot ideals and fuzzy dot H-ideals of BCH-algebras 被引量:4
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作者 PENG Jia-yin Key Laboratory of Numerical Simulation of Sichuan Province,Neijiang 641112,China Dept.of Math.,Neijiang Teachers College,Neijiang 641112,China. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2008年第1期101-106,共6页
The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are introduced, several appropriate examples are provided, and their some properties are investigated. The relations among fuzzy ideal, fuzzy H-id... The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are introduced, several appropriate examples are provided, and their some properties are investigated. The relations among fuzzy ideal, fuzzy H-ideal, fuzzy dot ideal and fuzzy dot H-ideals in BCH- algebras are discussed, several equivalent depictions of fuzzy dot ideal are obtained. How to deal with the homomorphic image and inverse image of fuzzy dot ideals (fuzzy dot H-ideals) are studied. The relations between a fuzzy dot ideal (fuzzy dot H-ideal) in BCH-algebras and a fuzzy dot ideal (fuzzy dot H-ideal) in the product algebra of BCH-algebras are given. 展开更多
关键词 BCh-algebra fuzzy (dot) ideal fuzzy (dot) h-ideal homomorphism.
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THE FIELD ALGEBRA IN HOPF SPIN MODELS DETERMINED BY A HOPF*-SUBALGEBRA AND ITS SYMMETRIC STRUCTURE
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作者 Xiaomin WEI Lining JIANG Qiaoling XIN 《Acta Mathematica Scientia》 SCIE CSCD 2021年第3期907-924,共18页
Denote a finite dimensional Hopf C*-algebra by H, and a Hopf *-subalgebra of H by H1. In this paper, we study the construction of the field algebra in Hopf spin models determined by H1 together with its symmetry. More... Denote a finite dimensional Hopf C*-algebra by H, and a Hopf *-subalgebra of H by H1. In this paper, we study the construction of the field algebra in Hopf spin models determined by H1 together with its symmetry. More precisely, we consider the quantum double D(H, H_(1)) as the bicrossed product of the opposite dual Hopˆ of H and H1 with respect to the coadjoint representation, the latter acting on the former and vice versa, and under the non-trivial commutation relations between H1 and Ĥ we define the observable algebra AH1. Then using a comodule action of D(H, H1) on AH1, we obtain the field algebra FH1, which is the crossed product AH1⋊D(H,H_(1)), and show that the observable algebra AH1 is exactly a D(H, H1)-invariant subalgebra of FH1. Furthermore, we prove that there exists a duality between D(H, H1) and AH1, implemented by a*-homomorphism of D(H, H_(1)). 展开更多
关键词 comodule algebra field algebra observable algebra COMMUTANT duality
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The tensor algebras of Yetter-Drinfeld module
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作者 Yanhua Wang 《上海师范大学学报(自然科学版)》 2014年第5期523-528,共6页
The antipode of a Yetter-Drinfeld Hopf algebra is an anti-algebra and anti-coalgebra map is proved. It is also proved that the tensor algebra of Yetter-Drinfeld Hopf module is a Yetter-Drinfeld Hopf algebra.
关键词 hopf algebra ANTIPODE comodule Yetter-Drinfeld hopf algebras
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The Structure Theorem for Module Coalgebras
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作者 WANG Yong ZHANG Liang-yun CAI Zhi-min 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期85-92,共8页
This paper,mainly gives the structure theorem for module coalgebras by a kind of new method,and deletes the condition that the antipode S of the Hopf algebra H is bijective.
关键词 hopf algebra hopf bicomodule comodule coalgebra smash coproduct module coalgebra
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On the Structure of the B-cocleft Module Coalgebra
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作者 焦争鸣 王栓宏 赵文正 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第4期44-47, ,共4页
In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is ... In this paper we develope the notions of crossed coproduct of Hopf algebras and study an equivalent theorem of generalized crossed coproduct of H weakly comodule coalgebras and H module coalgebras. The main result is to prove a structure theorem about B cocleft H module coalgebras. 展开更多
关键词 h module coalgebra h weakly comodule coalgebra crossed coproduct
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Construction of a class of H-pseudoalgebras
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作者 Liu Linlin Wang Shuanhong 《Journal of Southeast University(English Edition)》 EI CAS 2017年第4期517-520,共4页
Let H be a cocommutative Hopf algebra.First,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(i.e.left multiplication)of Hon itself into an adjoint action.Secondly,a class o f{... Let H be a cocommutative Hopf algebra.First,anew class//-pseudoalgebras o f H-pseudoalgebras are definedby changing the regular action(i.e.left multiplication)of Hon itself into an adjoint action.Secondly,a class o f{H,R)-pseudoalgebras are studied by generalizing the aboveconstruction when(H,R)is a quasitrianglar Hopf algebra.A tthe same time,the(H,R)-pseudoalgebra is constructed byboth the usual algebra and the tensor product o f(H,R)-pseudoalgebras.Finally,some examples of the(H,R)-pseudoalgebra are given explicitly,and the conditions for aHopf algebra to be an(H,R)-pseudoalgebra(resp.Hpseudoalgebra)are discussed. 展开更多
关键词 cocommutative hopf algebra h-pseudoalgebra h-pseudoalgebra ( h R) -pseudoalgebra
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ON INVERSES AND ALGEBRAIC LOOPS OF CO-H-SPACES
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作者 Dae-Woong LEE 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1193-1211,共19页
In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old... In this paper we study the properties of homotopy inverses of comultiplications and Mgebraic loops of co-H-spaces based on a wedge of spheres. We also investigate a method to construct new comultiplications out of old ones by using a group action. We are primarily interested in the algebraic loops which have inversive, power-associative and Moufang properties for some comultiplications. 展开更多
关键词 INVERSES co-h-spaces comultiplications basic (Whitehead) product hopf- hilton invariants algebraic loops inversivity power-associativity Moufang property
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Heisenberg模顶点代数的单商代数
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作者 李思佳 《哈尔滨师范大学自然科学学报》 CAS 2023年第2期6-8,共3页
运用H-模顶点代数的理论研究了素特征域上的Heisenberg顶点代数,证明了Heisenberg顶点代数的单商代数是H-模顶点代数并且存在唯一的非退化对称不变双线性型.
关键词 h-模顶点代数 heisenberg顶点代数 模顶点代数
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BCH-代数的模糊理想与模糊H-理想(英文) 被引量:15
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作者 胡宝清 何娟娟 刘敏 《模糊系统与数学》 CSCD 2004年第1期9-15,共7页
在BCK/BCI/BCC代数中Fuzzy理想被广泛研究,但在BCH-代数中还没有讨论过。在BCH-代数中引入了Fuzzy理想与FuzzyH-理想的概念,并讨论它们的性质。
关键词 BCh-代数 模糊理想 模糊h-理想 FUZZY理想
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赋范格H蕴涵代数和模糊格H蕴涵代数 被引量:5
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作者 赖家俊 徐扬 乔全喜 《计算机科学》 CSCD 北大核心 2008年第11期156-159,共4页
在范数的条件下扩充了格H蕴涵代数的概念,即赋范格H蕴涵代数,并讨论一些性质。然后将模糊集合论运用于赋范格H蕴涵代数,给出了模糊赋范格H蕴涵代数的定义,得到了一些基本性质。通过使用两个赋范格H蕴涵代数之间的映射定义了赋范格H蕴涵... 在范数的条件下扩充了格H蕴涵代数的概念,即赋范格H蕴涵代数,并讨论一些性质。然后将模糊集合论运用于赋范格H蕴涵代数,给出了模糊赋范格H蕴涵代数的定义,得到了一些基本性质。通过使用两个赋范格H蕴涵代数之间的映射定义了赋范格H蕴涵代数同态,且得到了一些性质。最后得到了在赋范格H蕴涵代数中的数列对于蕴涵距离是有界的结论。 展开更多
关键词 赋范格h蕴涵代数 模糊赋范格h蕴涵代数 赋范格h蕴涵代数同态 数列
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偏Doi-Hopf模的Maschke型定理 被引量:1
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作者 姜秀燕 王志忠 +1 位作者 金天坤 李秀丽 《吉林大学学报(理学版)》 CAS CSCD 北大核心 2011年第2期259-262,共4页
通过引入偏Doi-Hopf模积分映射的概念,证明了经典表示理论中的Maschke型定理在偏Doi-Hopf模条件下仍成立,即如果(H,A,C)是带有正规积分映射的偏Doi-Hopf数据,映射f:M→N是偏Doi-Hopf模同态,则只要f作为右A-模映射存在截面映射(收缩映射)... 通过引入偏Doi-Hopf模积分映射的概念,证明了经典表示理论中的Maschke型定理在偏Doi-Hopf模条件下仍成立,即如果(H,A,C)是带有正规积分映射的偏Doi-Hopf数据,映射f:M→N是偏Doi-Hopf模同态,则只要f作为右A-模映射存在截面映射(收缩映射),则f作为偏Doi-Hopf模映射也存在截面映射(收缩映射). 展开更多
关键词 偏Doi-hopf模 MASChKE型定理 h-余模代数
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广义系统状态反馈H_∞控制的一个条件 被引量:5
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作者 邢伟 张庆灵 +1 位作者 王启义 刘会立 《控制与决策》 EI CSCD 北大核心 2001年第2期219-221,225,共4页
采用状态空间方法 ,讨论一类广义系统的基于静态状态反馈的 H∞ 控制问题 ,得到了该问题满足可解性的一个充分必要条件 :某个基于系统参数阵的广义代数 Riccati不等式有满足一个广义约束的解。借助于广义代数 Riccati不等式的解 ,给出... 采用状态空间方法 ,讨论一类广义系统的基于静态状态反馈的 H∞ 控制问题 ,得到了该问题满足可解性的一个充分必要条件 :某个基于系统参数阵的广义代数 Riccati不等式有满足一个广义约束的解。借助于广义代数 Riccati不等式的解 ,给出一个所要求的且结构简单的控制器构造。若广义系统满足正交条件 ,则所得结论可进一步简化。 展开更多
关键词 广义系统 h∞范数 静态状态反馈 h∞控制理论
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格H蕴涵代数与格蕴涵代数类 被引量:16
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作者 徐扬 秦克云 《河北工程大学学报(自然科学版)》 CAS 1992年第3期139-143,共5页
本文研究了格H蕴涵代数的性质,给出了它的一些等价条件,讨论了格蕴涵代数类的真类问题和基数问题。
关键词 格蕴涵代数 h蕴涵代数
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离散广义系统基于动态输出反馈的H_∞控制 被引量:8
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作者 董心壮 张庆灵 郭凯 《系统工程与电子技术》 EI CSCD 北大核心 2003年第8期977-979,1036,共4页
考虑离散广义系统的动态输出反馈H∞ 控制问题。利用广义代数Riccati不等式 (GARI) ,给出离散广义系统存在正常动态输出反馈H∞ 控制器、使得闭环系统是容许的 ,且其从外界干扰输入到受控输出的传递函数矩阵具有H∞ 范数约束的充分必要... 考虑离散广义系统的动态输出反馈H∞ 控制问题。利用广义代数Riccati不等式 (GARI) ,给出离散广义系统存在正常动态输出反馈H∞ 控制器、使得闭环系统是容许的 ,且其从外界干扰输入到受控输出的传递函数矩阵具有H∞ 范数约束的充分必要条件。在适当的假设下 ,得到了正常动态输出反馈H∞ 控制器存在的必要条件以及一个充分条件 ,同时给出了相应的控制器构造 。 展开更多
关键词 离散广义系统 h∞范数 广义Riccati不等式 动态输出反馈
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弱Hopf群余模及其结构基本定理 被引量:2
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作者 王军昌 王顶国 《北京师范大学学报(自然科学版)》 CAS CSCD 北大核心 2006年第4期362-366,共5页
构造了弱Hopf群余代数,证明了弱Hopf群余模结构基本定理.
关键词 群余代数 hOPF群余代数 hOPF代数 群余模
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基于观测器的具有对称结构的广义大系统的H_∞分散控制 被引量:5
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作者 陈跃鹏 张庆灵 徐天群 《东北大学学报(自然科学版)》 EI CAS CSCD 北大核心 2001年第4期450-453,共4页
讨论具有对称结构的广义大系统的H∞ 分散控制问题· 通过设计基于状态观测器的状态反馈 ,借助于广义代数Riccati不等式 ,给出具有对称结构的闭环广义大系统的H∞ 分散控制的充要条件·
关键词 广义大系统 h∞分散控制 广义代数Riccati不等式 观测器
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