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A Duality Theorem for Hopf Comodule coalgebras

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Chinese Science Bulletin 1994年第15期39卷 1239-1244页

作者：王栓宏 Institute of Mathematics Fudan University Shanghai 200433 PRC

R. J. Blattner and S. Montgomery have proved the duality theorem of Hopf module algebras in Ref. [1]. This theorem contains duality for crossed product of von Neumann algebras. In 1977, R. K. Molnar introduced the concept of Hopf comodule coalgebras which is a dual notation of Hopf module algebra, and discussed their properties. However, the duality theorem of Hopf comodule coalgebras has not been proved yet. In this note we shall deal with this situation by defining the

关键词： Hopf algebra Hopf comodule coalgebra Hopf module coalgebra Smash coproduct.

Relation between decomposition of comodules and coalgebras

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Science China Mathematics 1997年第1期40卷 24-29页

作者：张寿传 Institute of Mathematics Fudan University Shanghai 200433 China

Let M be a C-comodule. It is clear that M and C can both be decomposed into a direct sum of the indecomposable subcoalgebras of C and subcomodules of M. The relation between the two decompositions is given

关键词： coalgebra comodule comodule component decomposition.

The Structure of Cocleft H-Module coalgebras

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Chinese Science Bulletin 1993年第20期38卷 1688-1692页

作者：刘贵龙 Institute of Mathematics Jilin University Changchun 130023 PRC

Y. Doi has investigated the H-comodule algebra since 1983. The structure theorem of cleft H-comodule algebra was given by Y. Doi and M. Takeuchi in 1986, i. e. if A is a cleft H-comodule algebra then A≌A0#σH as algebra. The dual notion of H-comodule algebra is H-module coalgebra. Y. Doi also studied the H-module coalgebra. However, he did not obtain the structure theorem of cocleft H-module coalgebra. In this note we introduce crossed coproducts which are the dual notion

关键词： Hopf algebra H-module coalgebra crossed coproduct

Morita theorems for Hopf comodule coalgebras

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Chinese Science Bulletin 1996年第12期41卷 969-972页

作者：刘贵龙 Department of Computer Application China University of Geosciences Beijing 100083 China

Morita context has been used to study algebra structure and category equivalenee sinceMorita theory was established in 1958. For an H-module algebra A, Cohen and Fischmanconstructed in 1986 a Morita contex [A^H,A,A,A#H] under the additional assumption thatH was unimodular and used the Morita context to study the Smash product A#H. In1990, Cohen, Fischman and Montgomery showed that fix ring A^H and smash product

关键词： pre-equivalence date Hopf comodule coalgebra Hopf module coalgebra.

Cosemisimple Coextensions and Homological Dimension of Smash Coproducts

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Acta Mathematica Sinica,English Series 2005年第3期21卷 563-568页

作者： Jia Gui ZHU Department of Mathematics University of Science and Technology of China Hefei 230026 P. R. China Department of Mathematics West Anhui University Lu'an 237012 P. R. China

Let H be a finite dimensional cosemisimple Hopf algebra, C a left H-comodule coalgebra and let C = C/C（H^＊）^＋ be the quotient coalgebra and the smash coproduct of C and H. It is shown that if C/C is a eosemisimple coextension and C is an injective right C-comodule, then gl. dim（the smash coproduct of C and H） = gl. dim（C） = gl. dim（C）, where gl. dim（C） denotes the global dimension of coalgebra C.

关键词： coalgebra Homological dimension Smash coproduct Hopf algebra

Some remarks on cotilting comodules

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Frontiers of Mathematics in China 2014年第3期9卷 699-714页

作者： Sujuan ZHANG Hailou YAO College of Applied Sciences Beijing University of Technology Beijing 100124 China Department of Mathematics and Physics Shijiazhuang Tiedao University Shijiazhuang 050043 China

We study cotilting comodules and f-cotilting comodules and give a description of localization of f-cotilting comodules and classical tilting comodules. First, we introduce T-cotilting injective comodules and their dimensions which are important for researching cotilting comodules. Then we characterize the localization in f-cotilting comodules, finitely copresented comodules, and classical tilting comodules. In particular, we obtain a localizing property about finitely copresented comodules.

关键词： coalgebra comodule localization

Dual Lie Bialgebra Structures of W-algebra W(2, 2) Type

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Acta Mathematica Sinica,English Series 2019年第10期35卷 1696-1714页

作者： Guang Ai SONG Yu Cai SU Xiao Qing YUE College of Mathematics and Information Science Shandong Technology and Business UniversityShandong 264005P.R.China School of Mathematical Sciences Tongji UniversityShanghai 200092P.R.China

In the present paper, we investigate the dual Lie coalgebras of the centerless W(2,2) algebra by studying the maximal good subspaces. Based on this, we construct the dual Lie bialgebra structures of the centerless W(2... 详细信息

关键词： W(2,2) algebra Lie bialgebra Lie coalgebra dual Lie bialgebra maximal good subspace

Diagrams of Hopf algebras with the Chevalley property

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Applied Mathematics(A Journal of Chinese Universities) 2016年第3期31卷 367-378页

作者： FAN Zhong-ping LU Di-ming YU Xiao-lan School of Mathematical Science Ocean University of China Department of Mathematics Zhejiang University Department of Mathematics Hangzhou Normal University

In this paper, we study non-cosemisimple Hopf algebras through their underlying coalgebra structure. We introduce the concept of the maximal pointed subcoalgebra/Hopf sub- algebra. For a non-cosemisimple Hopf algebra A with the Chevalley property, if its diagram is a Nichols algebra, then the diagram of its maximal pointed Hopf subalgebra is also a Nichols algebra. When A is of finite dimension, we provide a necessary and sufficient condition for A＇s diagram equaling the diagram of its maximal pointed Hopf subalgebra.

关键词： Hopf algebra coalgebra coradical Nichols algebra pointed Chevalley property

Decomposition of Comodules

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Science China Mathematics 1994年第8期37卷 946-953页

作者：邹小贵许永华 Institute of Mathematics Fudan University Shanghai 200433 PRC

It has been proved, using a special approach, that any comodules over a field can be uniquely decomposed into the direct sum of closed indecomposable subcomodules.

关键词： coalgebra comodule coradical wedge product.