Hopf Algebras and Quantum Groups最新文献

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Cyclic Cohomology of Coalgebras, Coderivations and De Rham Cohomology 余代数的循环上同调,协导与De Rham上同调
Hopf Algebras and Quantum Groups Pub Date : 2019-05-07 DOI: 10.1201/9780429187919-6
M. Farinati, A. Solotar
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引用次数: 2
Lifting of Nichols Algebras of Type A 2 and Pointed Hopf Algebras of Order p 4 a2型Nichols代数和p4阶点Hopf代数的提升
Hopf Algebras and Quantum Groups Pub Date : 2019-05-07 DOI: 10.1201/9780429187919-1
N. Andruskiewitsch, H. Schneider
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引用次数: 5
On Regularity of the Algebra of Covariants for Actions of Pointed Hopf Algebras on Regular Commutative Algebras 点Hopf代数作用于正则交换代数的协变代数的正则性
Hopf Algebras and Quantum Groups Pub Date : 2019-05-07 DOI: 10.1201/9780429187919-14
A. Tyc
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引用次数: 0
A Survey on Multiplier Hopf Algebras 关于乘数Hopf代数的综述
Hopf Algebras and Quantum Groups Pub Date : 2019-05-07 DOI: 10.1201/9780429187919-15
Yinhuo Zhang
{"title":"A Survey on Multiplier Hopf Algebras","authors":"Yinhuo Zhang","doi":"10.1201/9780429187919-15","DOIUrl":"https://doi.org/10.1201/9780429187919-15","url":null,"abstract":"In this paper, we generalize Majid’s bicrossproduct construction. We start with a pair (A,B) of two regular multiplier Hopf algebras. We assume that B is a right A-module algebra and that A is a left B-comodule coalgebra. We recall and discuss the two notions in the first sections of the paper. The right action of A on B gives rise to the smash product A#B. The left coaction of B on A gives a possible coproduct ∆# on A#B. We will discuss in detail the necessary compatibility conditions between the action and the coaction for ∆# to be a proper coproduct on A#B. The result is again a regular multiplier Hopf algebra. Majid’s construction is obtained when we have Hopf algebras. We also look at the dual case, constructed from a pair (C,D) of regular multiplier Hopf algebras where now C is a left D-module algebra while D is a right C-comodule coalgebra. We will show that indeed, these two constructions are dual to each other in the sense that a natural pairing of A with C and of B with D will yield a duality between A#B and the smash product C#D. We show that the bicrossproduct of algebraic quantum groups is again an algebraic quantum group (i.e. a regular multiplier Hopf algebra with integrals). The -algebra case will also be considered. Some special cases will be treated and they will be related with other constructions available in the literature. Finally, the basic example, coming from a (not necessarily finite) group G with two subgroups H and K such that G = KH and H ∩K = {e} (where e is the identity of G) will be used throughout the paper for motivation and illustration of the different notions and results. The cases where either H or K is a normal subgroup will get special attention. March 2009 (Version 2.1) 1 Department of Mathematics, Hasselt University, Agoralaan, B-3590 Diepenbeek (Belgium). E-mail: Lydia.Delvaux@uhasselt.be 2 Department of Mathematics, K.U. Leuven, Celestijnenlaan 200B (bus 2400), B-3001 Heverlee (Belgium). E-mail: Alfons.VanDaele@wis.kuleuven.be 3 Department of Mathematics, Southeast University, Nanjing 210096, China. E-mail: shuanhwang@seu.edu.cn","PeriodicalId":403117,"journal":{"name":"Hopf Algebras and Quantum Groups","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133238568","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
The Coquasitriangular Hopf Algebra Associated to a Rigid Yang–Baxter Coalgebra 与刚性Yang-Baxter协代数相关的协拟三角Hopf代数
Hopf Algebras and Quantum Groups Pub Date : 2019-05-07 DOI: 10.1201/9780429187919-13
M. Takeuchi
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引用次数: 0
Survey of Cross Product Bialgebras 叉积双代数的综述
Hopf Algebras and Quantum Groups Pub Date : 2019-05-07 DOI: 10.1201/9780429187919-2
Y. Bespalov, B. Drabant
{"title":"Survey of Cross Product Bialgebras","authors":"Y. Bespalov, B. Drabant","doi":"10.1201/9780429187919-2","DOIUrl":"https://doi.org/10.1201/9780429187919-2","url":null,"abstract":"","PeriodicalId":403117,"journal":{"name":"Hopf Algebras and Quantum Groups","volume":"170 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114188881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Generalized Power Map for Hopf Algebras Hopf代数的广义幂映射
Hopf Algebras and Quantum Groups Pub Date : 2019-05-07 DOI: 10.1201/9780429187919-8
Y. Kashina
{"title":"A Generalized Power Map for Hopf Algebras","authors":"Y. Kashina","doi":"10.1201/9780429187919-8","DOIUrl":"https://doi.org/10.1201/9780429187919-8","url":null,"abstract":"","PeriodicalId":403117,"journal":{"name":"Hopf Algebras and Quantum Groups","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125966509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Separable Functors for the Category of Doi–Hopf Modules II Doi-Hopf模类的可分函子II
Hopf Algebras and Quantum Groups Pub Date : 2019-05-07 DOI: 10.1201/9780429187919-5
S. Caenepeel, B. Ion, G. Militaru, Shenglin Zhu
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引用次数: 0
A Monta–Takeuchi Context for Graded Coalgebras 分级代数的Monta-Takeuchi背景
Hopf Algebras and Quantum Groups Pub Date : 2019-05-07 DOI: 10.1201/9780429187919-3
C. Boboc
{"title":"A Monta–Takeuchi Context for Graded Coalgebras","authors":"C. Boboc","doi":"10.1201/9780429187919-3","DOIUrl":"https://doi.org/10.1201/9780429187919-3","url":null,"abstract":"","PeriodicalId":403117,"journal":{"name":"Hopf Algebras and Quantum Groups","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116704478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Associated Varieties for Classical Lie Superalgebras 经典李超代数的相关变分
Hopf Algebras and Quantum Groups Pub Date : 2019-05-07 DOI: 10.1201/9780429187919-9
I. Musson
{"title":"Associated Varieties for Classical Lie Superalgebras","authors":"I. Musson","doi":"10.1201/9780429187919-9","DOIUrl":"https://doi.org/10.1201/9780429187919-9","url":null,"abstract":"","PeriodicalId":403117,"journal":{"name":"Hopf Algebras and Quantum Groups","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127155741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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