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weak hopf algebras Corresponding to Borcherds-Cartan Matrices

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Acta Mathematica Sinica,English Series 2007年第10期23卷 1729-1744页

作者： Li Xia YE Zhi Xiang WU Xue Feng MEI Department of Computer Science Zhejiang Education Institute Hangzhou 310012 P. R. China Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China Department of Mathematics Zhejiang Education Institute Hangzhou 310012 P. R. China

Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d（y）, which is a weak hopf algebra. We also study t... 详细信息

关键词： weak hopf algebra weak quantum generalized Kac-Moody algebra highest weight module weak A-form

TWISTED PRODUCTS AND SMASH PRODUCTS OVER weak hopf algebraS

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Acta Mathematica Scientia 2004年第2期24卷 247-258页

作者：张良云陈惠香李金其 DepartmentofMathematics NanjingAgriculturalUniversityNanjing210095China

This paper gives a sufficient and necessary condition for twisted products to be weak hopf algebras, moreover, gives a description for smash products to be weak hopf algebras. It respectively generalizes ***'s major r... 详细信息

关键词： weak bialgebra weak hopf algebra twisted product smash product

Twisting theory for weak hopf algebras

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Applied Mathematics(A Journal of Chinese Universities) 2008年第1期23卷 91-100页

作者： CHEN Ju-zhen ZHANG Yan WANG Shuan-hong Dept. of Math. Southeast Univ. Nanjing 210096 China.

The main aim of this paper is to study the twisting theory of weak hopf algebras and give an equivalence between the （braided） monoidal categories of weak hopf bimodules over the original and the twisted weak hopf a... 详细信息

关键词： weak hopf algebra weak hopf bimodule twisting theory.

On Quasi-Bicrossed Products of weak hopf algebras

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Acta Mathematica Sinica,English Series 2004年第2期20卷 305-318页

作者： FangLI DepartmentofMathematics ZhejiangUniversityHangzhou310028P.R.China

The aim of this paper is to study quasi-bicrossed products and a especially quantum quasi-doubles. Firstly, we construct one new kind of quasi-bicrossed products by weak hopf algebras and then devote a brief discussion to this matter. And, we discuss the conditions for quasi-bicrossed products to possess the structure of almost weak hopf algebras, containing the case of a special smash product. At the end, we give some properties on the quantum quasi-double, respectively on the quasi- R-isomorphism, the representation-theoretic interpretation and the regularity of the quasi-R-matrix.

关键词： weak hopf algebra Bicrossed product Quantum double

SYMMETRIES IN YETTER-DRINFELD CATEGORIES OVER weak hopf algebraS

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Acta Mathematica Scientia 2008年第4期28卷 870-876页

作者：高楠 Department of Mathematics Shanghai Jiao Tong University

This article is devoted to the study of the symmetry in the Yetter-Drinfeld category of a finite-dimensional weak hopf *** generalizes the corresponding results in hopf algebras.

关键词： weak hopf algebra Yetter-Drinfeld module symmetry

Construct weak hopf algebras by Using Borcherds Matrix

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Acta Mathematica Sinica,English Series 2009年第8期25卷 1337-1352页

作者： Zhi Xiang WU Department of Mathematics Zhejiang University Hangzhou 310027 P. R. China

We define a new kind quantized enveloping algebra of a generalized Kac-Moody algebra by adding a new generator J satisfying jm = j for some integer m. We denote this algebra by wUqT（A）. This algebra is a weak hopf algebra if and only if m = 2,3. In general, it is a bialgebra, and contains a hopf subalgebra. This hopf subalgebra is isomorphic to the usual quantum envelope algebra Uq （A） of a generalized Kac-Moody algebra A.

关键词： generalized Kac-Moody algebras irreducible representation weak hopf algebra

A Maschke Type Theorem for weak hopf algebras

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Acta Mathematica Sinica,English Series 2008年第12期24卷 2065-2080页

作者： J.N.ALONSOLVAREZ J.M.FERNNDEZVILABOA R.GONZLEZRODRíGUEZ A.B.RODRíGUEZRAPOSO Departamento de Matemáticas Universidad de Vigo. Lagoas-Marcosende Vigo. E-36200 Spain Departamento de lxebra. Universidad de Santiago de Compostela Santiago de Compostela. E-15771 Spain Departamento de Matemdtica Aplicada Ⅱ. Universidad de Vigo. Lagoas-Marcosende Vigo. E-36310 Spain Departamento delxebra Universidad de Santiago de CompostelaSantiago de Compostela E-15771 Spain

In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the hopf algebra setting. Also, from these results, we deduce a version of Maschke＇s Theorem for （H, B）-hopf modules associated with a weak hopf algebra H and a right H-comodule algebra B.

关键词： Monoidal category weak hopf algebra hopf modules Maschke Theorem

Crossed Products over weak hopf algebras Related to Cleft Extensions and Cohomology

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Chinese Annals of Mathematics,Series B 2014年第2期35卷 161-190页

作者： José Nicanor Alonso áLVAREZ José Manuel Fernández VILABOA Ramón González RODRíGUEZ Departamento de Matemáticas Universidad de VigoCampus Universitario Lagoas-Marcosende Departamento de álxebra Universidad de Santiago de Compostela Departamento de Matemática Aplicada II Universidad de VigoCampus Universitario Lagoas-Marcosende

The authors present the general theory of cleft extensions for a cocommutative weak hopf algebra H. For a right H-comodule algebra, they obtain a bijective corre- spondence between the isomorphisms classes of H-cleft extensions AH → A, where AH is the subalgebra of coinvariants, and the equivalence classes of crossed systems for H over AH. Finally, they establish a bijection between the set of equivalence classes of crossed systems with a fixed weak H-module algebra structure and the second cohomology group H2φZ（AH）（H, Z（AH））, where Z（AH） is the center of AH.

关键词： Monoidal category weak hopf algebra Cleft extension weak crossedproduct Sweedler cohomology for weak hopf algebras

Nichols algebras over weak hopf algebras

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Applied Mathematics(A Journal of Chinese Universities) 2018年第1期33卷 107-126页

作者： WU Zhi-xiang School of Mathematical Science Zhejiang University

In this paper, we study a Yetter-Drinfeld module V over a weak hopf algebra *** the category of all left H-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak hopf algebra H, and a series of weak hopf algebras. Some results of [8] are generalized.

关键词： quantum enveloping algebra Nichols algebra weak hopf algebra