Two-Parameter Weak Hopf Algebras Corresponding to Borcherds-Cartan Matrix

相应于Borcherds-Cartan矩阵的双参数弱Hopf代数(英文)

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摘要 In this paper a class of two-parameter weak Hopf algebras wrτ,s(g) corresponding to Borcherds-Cartan matrix is constructed. This class consists of noncommutative and noncocommutative weak Hopf algebras but not Hopf algebras. It can be viewed as a generalized class of one-parameter weak Hopf algebras wUq(g). In this paper a class of two-parameter weak Hopf algebras wrτ,s（g） corresponding to Borcherds-Cartan matrix is constructed. This class consists of noncommutative and noncocommutative weak Hopf algebras but not Hopf algebras. It can be viewed as a generalized class of one-parameter weak Hopf algebras wUq（g）.

作者艾春瑞杨士林

机构地区 Department of Mathematics College of Applied Sciences

出处《Journal of Mathematical Research and Exposition》 CSCD 2009年第6期961-973,共13页 数学研究与评论（英文版）

基金 the National Natural Science Foundation of China (Nos.10671016 10771014) the Foundation of Beijing Educational Committee (No.KM200710005013)

关键词 Kac-Moody algebras weak antipode Borcherds-Cartan matrix. 弱Hopf代数 Cartan矩阵赫兹双参数矩阵构造非交换嘉当

分类号 O152.5 [理学—基础数学]

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1DU Jie, PARSHALL B, WANG Jianpan. Two-parameter quantum linear groups and the hyperbolic invariance ofq-Schur algebras [J]. J. London Math. Soc. (2), 1991, 44(3): 420-436.
2DOBREV V K, PARASHAR P. Duality for multipararnetric quantum GL(n) [J]. J. Phys. A, 1993, 26(23): 6991-7002.
3BERGERON N, GAO Yun, HU Naihong. Drinfel'd doubles and Lusztig's symmetries of two-parameter quantum groups [J]. J. Algebra, 2006, 301(1): 378-405.
4BOHM G, NILL F, SZLACHANYI K. Weak Hopfalgebras. L Integral theory and C*-structure [J]. J. Algebra, 1999, 221(2): 385-438.
5HAYASHI T. An algebra related to the fusion rules of Wess-Zumino-Witten models [J]. Lett. Math. Phys., 1991, 22(4): 291-296.
6YAMANOUGHI T. Duality for generalized Kac algebras and a characterization of finite groupoid algebras [J]. J. Algebra, 1994, 163(1): 9-50.
7LI Fang. Weak Hopf algebras and some new solutions of the quantum Yang-Baxter equation [J]. J. Algebra, 1998, 208(1): 72-100.
8YANG Shilin. Weak Hopf algebras corresponding to Caftan matrices [J]. J. Math. Phys., 2005, 46(7): 073502.
9BORCHERDS R. E. Generalised Kac-Moody algebras [J]. J. Algebra, 1988, 115(2): 501-512.
10WU Zhixiang. A class of Weak Hopf algebras related to a Borcherds-Cartan matrix [J]. J. Phys. A, 2006, 39(47): 14611-14626.

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2候波,张子龙,蔡炳苓,李燕.MORITA CONTEXT OF WEAK HOPF ALGEBRAS[J].Acta Mathematica Scientia,2011,31(3):1133-1141.
3高楠.SYMMETRIES IN YETTER-DRINFELD CATEGORIES OVER WEAK HOPF ALGEBRAS[J].Acta Mathematica Scientia,2008,28(4):870-876.
4邵红能.陈省身:数学当歌人生几何[J].科学24小时,2012(10):46-48.
5无,陆柱家(译),袁向东(校).Henri Cartan，1904—2008[J].数学译林,2008,27(3):273-273.
6曹海军,李方,张棉棉.CONSTRUCTING POINTED WEAK HOPF ALGEBRAS BY ORE-EXTENSION[J].Acta Mathematica Scientia,2014,34(2):252-262.
7薛有才.欧高黎嘉陈——欧几里得、高斯、黎曼、嘉当、陈省身五位几何大师的数学业绩述评[J].运城高等专科学校学报,2001,19(3):56-58.
8CHEN Ju-zhen ZHANG Yan WANG Shuan-hong.Twisting theory for weak Hopf algebras[J].Applied Mathematics(A Journal of Chinese Universities),2008,23(1):91-100. 被引量：1
9唐宝民,姚远.一生只做一件事的智慧[J].华人时刊,2011(12):69-69.
10唐宝民.一生只做一件事[J].科学大观园,2011(9):1-1.

Journal of Mathematical Research and Exposition

2009年第6期

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Two-Parameter Weak Hopf Algebras Corresponding to Borcherds-Cartan Matrix

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