2665威尼斯

2665威尼斯欢迎您?,今天是?:?2018年6月8日 English |? 简体中文
李立斌
发布日期:2018-09-04

姓名:李立斌

研究领域:代数学、学科教学(数学);研究兴趣:

Representation theory in Hopf algebras, Ringel-Hall algebras and non-commutative algebraic geometry

Decoding theory and Ring theory

Schur algebras, classical groups and invariant theory

Weyl algebras and isomorphism problems

Tensor category

教育背景:

1997.9–2000.6, 中国科学技术大学, 基础数学, 博士;

1985.9–1988.6, 扬州师范学院, 基础数学, 硕士;

1981.9–1985.6, 扬州师范学院, 数学, 学士

工作经历:

2015.7-至今, 扬州大学, 2665威尼斯,教授、博士生导师

● 2018.7-2018.7, Hasselt大学, 数学系, 访问教授

2016.1-2016.2, 南洋理工大学, 数学系, 访问教授

2014.4-2014.7, Antwerp大学, 数学系, 访问教授

2012.2-2012.3, Hasselt大学, 数学系, 访问教授

2012.4-2012.5, Stuttgart大学, 数学系, 访问教授

2010.8-2010.9, Tsukubu大学, 数学系, 访问教授

2007.1-2007.3, Koln大学, 数学系, 访问教授

2000.12-2001.11, Bielefeld, 数学系, 助理研究员

1999.9-2005.8, 扬州大学, 数学学院, 副教授

1990.9-1999.8, 扬州工学院, 基础部, 讲师

1988.7-1990.8, 扬州工学院, 基础部, 助教

2004.6-2005.2, Leicester大学, 博士后, 合作导师: Steffen Koenig

2000.12-2001.12: 助理研究员(VW) , Bielefeld 大学 (指导老师: C. M. Ringel).

教学经历:1988年任职以来,一直在教学一线任教,主讲的课程主要有:

本科生课程:近世代数、线性代数、高等数学。

研究生课程:基本代数、 Lie代数、Hopf代数、Galois理论、量子群、群与代数表示、Kac-Moody李代数、Quiver表示、张量范畴。

科研与人才项目:

国家自然科学基金面上项目,量子群和张量范畴形变理论中的若干问题,118710632019/01-2022/12,53万元,在研,主持。

国家自然科学基金国际合作与交流项目,1711530703,有限张量范畴的形变,2018/01-2019/12,10万元,在研,参加。

国家自然科学基金面上项目,11471282,非半单Hopf代数的Green环及相关问题,2015/01-2018/12,68万元,已结题,主持。

国家天元基金,11526026,第十四届全国代数学学术会议,2016/01-2016/12, 8万元,已结题,参加。

国家自然科学基金面上项目,11171291,若干Hopf代数的表示及相关不变量,2012/01-2015/12,45万元,已结题,参加。

高等学校博士学科点专项科研基金, 20123250110005,关于几类非半单Hopf代数的表示环的研究, 2012/01-2014/12, 12万元,已结题,主持。

国家自然科学基金面上项目,10771182,量子超代数的结构、表示与实现,2008/01-2010/12,25万元,已结题,主持。

国家自然科学基金面上项目,10241002,李超代数的量子化代数与Ringle-Hall代数,2003/01-2003/12,4万元,已结题,主持。

国家自然科学基金面上项目,10071078,典型群和Chevalley群的子群结构,2001/01-2003/12,11万元,已结题,参加。

发表文章:在《Journal of Algebra》、《Alg. Rep.Theory》、《Archiv der Mathematik》等国内外刊物上发表论文60余篇,主要代表作有:.

On the centers of quantum groups of A_n -type, Sci. China Math, 61(2018): 287-294, (joint with L. M. Xiao and Y. H. Zhang).

基于Benson-Carlson商环的双Frobenius代数的构造, 中国科学中文版, 28(2018),no.48,471-48, (joint with Z. H. Wang and Y. H. Zhang)

●Verlinde 模性范畴上的Casimir 数及其应用, 数学学报中文版,61(2018), no.1,59-66, (joint with Z.H Wang)

●Nilpotent Elements in Green Rings of a Class of Pointed Tensor Categories of Finite Type, Bulletin of the Malaysian Mathematical Sciences Society, 41(2018),1495-1506, (joint with C. T. Yuan and H. Yao)

Irreducible Z_+-modules of near-group fusion ring K(Z_3,3), 947–966, (joint with C.T. Yuan and R. J. Zhao)

Representations of the quantum matrix algebra M_q(2) arising from Ore extensions. 293–306, (joint with Z. H. Wang).

Double Frobenius algebras. 399–415, (joint with Z. H. Wang).

A criterion for the Jacobson semisimplicity of the Green ring of a _finite tensor category, Glasg. Math. J, 60(2018): 253-272, (joint with Z. H. Wang and Y. H. Zhang).

Green rings of pointed rank one Hopf algebras of non-nilpotent type, J. Algebra, 449(2016):108 -137, (joint with Z. H. Wang and Y. H. Zhang).

Integral almost square-free modular categories, J. Alg. App, 16(2016): 1750104, 14 pp,(joint with J. C. Dong and L. Dai).

Green rings of pointed rank one Hopf algebras of nilpotent type. Algebr. Represent. Theory, 17 (2014), 1901-1924, (joint with Z. H. Wang and Y. H. Zhang).

The Green rings of the generalized Taft Hopf algebras, Comtemporary Mathematics, 585(2013), (joint with Y. H. Zhang).

On the indecompsoable modules of Uq(sl(2)) constructed by Ore- extension, Acta.Math.Sinica (English Series), 29(2013), 1391-1400, (joint with Z. H. Wang).

On holonomic A_1-module k[x, p^-1], J. Math, 33(2013), 773-780.

Quantum Weyl polynomials and the center of quantum group Uq(sl_3),  Alg. Colloquium, 19(2012),525-532, (joint with J. Y. Wu and M. L. Zhu).

Weakly normal rings, Turk. J. Math, 36(2012), 47-57, (joint with J. C. Wei).

Quantum symmetric polynomials and the center of U_q(sl_4), Sci. China. Math, 54(2011), 55-64, (joint with J. Y. Wu and J. C. Wei).

Poincare Series and an application to Weyl algebras, Acta. Math. Scienta, 31(B)( 2011}, 459-467, (joint with Z. H. Wang).

Nilpotent elements and reduced rings, Turk. J. Math, 35(2011), 341-353, (joint with J. C. Wei).

Quasitriangular Hopf group coalgebras and Braided monoidal categories, Arab J. Sci Eng, 36(2011), 1063-1070, (joint with H. X. Chen and  M. L. Zhu).

Coquasitriangular Hopf group coalgebras and Braided monoidal categories Front. Math. China, 6(2011),1009-1020 (joint with H. X. Chen and M. L. Zhu).

Action of Uq(g) on its positive part U^+(g), J. Math. Res and Exp, 31(2011), 665-674, (joint with Z. H. Wang).

The equitable presentation for the quantum algebra Uq(f(k)), Quantized algebra and Physics (edited by M. L. Ge, C. M. Bai and N. H. Jing),World Scentific, Vol 8, 187-200,Joint with Y. Pan

Quasi-normal rings, Comm.Alg,  38(2010), 1855-1868(joint with J.C. Wei).

Ore extension of Quasitriangular Hopf algebras, Acta.Math. Sci, 29(2009), 1572-1579, (joint with Z. H. Wang).

MC2 rings and WQD rings, Glasg. Math. J, 51(2009), 691-702.(joint with J. C. Wei).

Strong DS rings, Southeast Asian Bull. Math, 33(2009), 375-390, (joint with J. C. Wei).

Stable ideals of the locally finite subalgebra of the quantum group U_q(f(K)), J. Math. Study, 42(2009), 45—52, (joint with X. J.Zhang)

A class of standard bases of polynomial algebras and its applications, J. Math. Res. Exposition, 29(2009),191—201, (joint with J. C. Dong).

The Killing form of a Hopf algebra and its radical. Arab. J. Sci. Eng. Sect. Theme Issues, 33(2008), 553—559, (joint with Z. H. Wang and H. X. Chen).

Frobenius property of a cosemisimple Hopf algebra,  J. Math. Res. Exposition, 27(2007), 469—473, (joint with J. C. Dong and L. Dai)

Comparing Lusztig's algebras and Hall algebras at v=-1, J. Algebra, 305(2006), 775-788, (joint with S. Koenig).

The center of the quantum group U_q({\rm osp}(1,2)). J. Math.  26 (2006), 569—573, (joint with Y. Zhang)

Presentation of Quantum generalized Schur algebra, Algebra and its applications, 4(2005),567-575.

Self-dual Hopf quiversComm.Algebra, 33(2005), 4505-4516. (joint with H. L. Huang and Y. Ye).

Unique decomposition of the ideals in quantum group U_q(sl(2)), Chinese Ann. Math. Ser. A, (2004), 817-824, (joint with J. H. Sun).

Constructing indecomposable representations over quantum group U_q(sl(2)).  Archiv der Mathematik. 80 (2003), 578-585.

The coradical filtration for double Ringel-Hall Algebras. Comm. Alg. 31 (2003), 1545-1559.

Graded antisimple primitive radical. Acta Math. Sin. Eng. Ser. 18 (2002), 505-512, (joint with J. C. Wei).

Colored Ringel-Hall algebras: applications to quantized Borcherds  superalgebras. Representations of algebras. Proceedings of the Ninth  International conference, Beijing, 2000, 308-320, Beijing Normal University Press, 2002. (joint with P. Zhang)

Quantum groups by Ore extension associated with group algebras.  J. Math. Res. Exposition. 2 (2002), 54-61. (joint with  S. Z. Li ).

K_1-groups of finite dimensional path algebras. Acta Math. Sin.(Eng. Ser).   17(2001), 273-276, (joint with X. J. Guo).

Irreducible representation of quantum group V_q(sl(2)), J. Math. 21(2001), 155-160. (joint with J. C. Wei).

The non-negative part of quantum group  U_q(sl(2). J. Math. Study.  34(2001), 43-46, (joint with G. G. Fu).

Weight property for ideals of U_q(sl(2)). Comm. Algebra. 29(2001), 4853-4870, (joint with P. Zhang).

Quantum comodule approach the solution of the quantum Yang-Baxter equation. Acta. Math. Sci. (English Ed). 20, 201-210, (joint with S. Z. Li).

Quantum Yang-Baxter modules and a generalized notion of the Drinfeld  quantum double. Representations and quantizations (Shanghai,1998), 317-328, China. High. Educ. Press and  Springer, 2000, (joint with S. Z. Li).

Quantum adjoint action for U_q(sl(2)). Algebra Colloq. 7(2000), 369-379, (joint with P. Zhang).

Twisted Hopf algebras, Ringel-Hall algebras and Green's categories. With an appendix by the referee. J. Algebra. 231}(2000), 713-743, (joint with P. Zhang)

 Solution to the Yang-Baxter equation and quantum Yang-Baxter H-comodules.

Math. Res. Exposition. 19((1999), 649-653, (joint with J. C. Wei).

联系地址:2665威尼斯,邮编:225002

电子邮箱:lbli@yzu.edu.cn





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