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## Representation of Degree n for Cosemisimple Hopf Algebras

WU Mei-yunCollege of Science,Nantong University,Nantong Jiangsu 226007,China
Let H be a cosemisimple Hopf algebra over an algebrically closed field k and n an odd positive integer.It is shown that if H only has simple distinct subcoalgebra of odd dimension which is no more than(2n-1)~2 except that H has a simple subcoalgebra of dimension n~2,then H contains either a grouplike element of order 3 or 5,or 7,…,or n,or there is a n-dimension self conjugate basic element x_n with x~2_n=1+x_3+x_5+…+x_(2n-1),where x_3,x_5,…,x_(2n-1) are basic elements of g(H) with ｜x_3｜=3,｜x_5｜=5,…,(｜x_(2n-1)｜=2n-1.)
【Fund】： 国家自然科学基金资助项目(10471121);; 南通大学自然科学基金资助项目(05Z006)
【CateGory Index】： O153.3
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 【Co-references】
 Chinese Journal Full-text Database 4 Hits
 1 LI Wei, LIU He (Mathematical College, Sichuan University,Chengdu 610064, China);GENERALIZED VECTOR SPACE CATEGORIES AND THE n-EXTENSION OF ALGEBRAS[J];Journal of Sichuan University (Natural Science Edition);2000-05 2 ZHAO Shi-yin(Department of Teachers Education,Suqian College,Suqian 223800,China);Hopf π-coalgebra and unilateral π-coideal[J];Journal of Shandong University of Technology(Natural Science Edition);2009-02 3 WU Meiyun~* TANG Qiulin~* *College of Science,Nantong University,Nantong 226007,Jiangsu,China.;Classification of Hopf Path Coalgebras over Dihedral Group[J];Chinese Annals of Mathematics;2007-05 4 Yao Hailou  Ping Yanru (Department of Applied Mathematics, Beijing Polytechnic University, Beijing 100022, China);Representation Type of Endomorphism Algebras of Exceptional Sequences of Type A n[J];ACTA MATHEMATICA SINICA;1998-05
 【Secondary References】
 Chinese Journal Full-text Database 4 Hits
 1 TANG Shuai1,WANG Zhihua2(1.Department of Mathematics and Physics,Taizhou Teachers College,Jiangsu Taizhou 225300,China;2.Taizhou College,Nanjing Normal University,Jiangsu Taizhou 225300,China);Killing Radicals of a Family of Hopf Algebras[J];Journal of Hebei Normal University(Natural Science Edition);2012-01 2 ZHAO Shi-yin1,2 (1.Department of Teachers Education,Suqian College,Suqian 223800,China;2.School of Mathematics,Yangzhou University,Yangzhou 225002,China);π-Algebra and π-Submodule[J];Jilin Normal University Journal(Natural Science Edition);2010-02 3 ZHAO Shi-yin1,2,YU Ai-jun1(1.Department of Teachers Education,Suqian College,Suqian 223800,China; 2.School of Mathematics,Yangzhou University,Yangzhou 225002,China);π-module Subcoalgebra[J];Journal of Shanxi University(Natural Science Edition);2011-02 4 ZHAO Shiyin;Department of Teachers Education,Suqian College;;π-H-module Algebra and π-H-module Ideal[J];Journal of Shanxi University(Natural Science Edition);2014-02
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