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李立斌

领域:新一代信息技术产业 学校:扬州大学职称:教授

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 problemЦᯬ...

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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, 数学科学学院,教授、博士生导师 ● 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).

项目课题经历

●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,11871063,2019/01-2022/12,53万元,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。

论文、成果、著作等

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), Front. Math. China 13 (2018), no. 4, 947–966, (joint with C.T. Yuan and R. J. Zhao)

●Representations of the quantum matrix algebra M_q(2) arising from Ore extensions. Southeast Asian Bull. Math. 42 (2018), no. 2, 293–306, (joint with Z. H. Wang).

●Double Frobenius algebras. Front. Math. China 13 (2018), no. 2, 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 quivers,Comm.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).

专利、著作版权等

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