Fang Li, Professor of Department of Mathematics, Zhejiang University



1988-1991: Doctorate, Department of Mathematics, Lanzhou University, Lanzhou, P.R.China

1985-1988: Master, Department of Mathematics, South China Normal  University, Guangzhou, P.R.China

1981-1985: Bachelor, Department of Mathematics, Hangzhou Normal University, Hangzhou, P.R.China



Representation of algebra, Hopf algebra, Ring theory, Quantum group, Groups and

semigroups and their representations, Matrix theory



Feb. 2001-today: Reviewing the evaluations of proposals for the National Natural Science Foundation of China and the National Science Foundation of USA

Mar. 1998-today: Professor, Department of Mathematics, Zhejiang University, Hangzhou, China

Jul. 1997-today: Member of European Mathematical Society

Jan. 1995-today: Member of American Mathematical Society

Jun. 1994-today: Reviewer for Mathematical Reviews, USA

Jul. 1993-today: Reviewer for Zentralblatt fur Mathematik, Germany

Dec.2003-Feb.2004:Recipient of a Raybould Fellowship, Department of Mathematics, University of Queensland, Brisbane, Australia;Visiting Department of Mathematics, University of New South

Nov.2001-Jan.2002: Visiting scholar, Deapartment of Mathematics, University of Bielefeld, Bielefeld, Germany 

Jul.2001-Oct. 2001: Visiting scholar, Institute of Mathematics, China Academy of Sciences, Beijing, China

Jan. 1994-2001: Member of China Centre of Advanced Science and echnology

Jul.2000-Sept.2000: (i) Visiting scholar, Department of Mathematics, University of Tasmania, Hobart, Australia; Visiting scholar, Department of Mathematics, University of Sydney, Sydney, Australia

May 2000: Visiting scholar, Nankai Institute of Mathematics, Nankai University, Tianjin, China

Oct. 1999-Dec. 1999: Visiting scholar, Department of Mathematics, City University of Hong Kong, Hong Kong, China

Jul. 1998-Sept. 1998: Visiting scholar, Institute of Mathematics, China Academy of Science, Beijing, China

Oct. 1993-Jan. 1998: Associate professor (prior to Apr. 1996), Professor (since Apr. 1996)Dept. of Applied Math., Southeast University, Nanjing, China

Sept. 1991-Oct. 1993: Post-doctor and associate professor, Dept. of Physics, Lanzhou University, Lanzhou, China

Feb. 1992-Jun.1992: Visiting scholar, Graduate School, China Academy of Science, Beijing, China



  1. The actions of semigroups and the theory of semigroup rings: supported by the National Natural Science Foundation of China (No.19501007)(from 1996 to 1998, RMB$30000);
  2. Quantum groups and the categorical theory of its representations and solutions of Yang-Baxter equation: supported by the National Natural Science Foundation of China (No.19971074)(from 2000 to 2002, RMB$95000) 
  3. Quantized Algebraic (Super-)Structures and Applications: supported by the International Award from Australian Research Council (No. LX0346913)(from 2002 to 2004, Aust$66000)
  4. Algebraic structures of quantum groups and symmetric systems, supported by the Natural Science Foundation of  Zhejiang Province (No.102028) (from 2003 to 2005, RMB$40000)
  5. Project supported by the Program for New Century Excellent Talents in University of China (No.04-0522)(from 2005 to 2007, RMB$500000)
  6. Characterization of associative algebras through quivers and classification  of representation type of Hopfalgebras and their relationship with the theory of quanmtum groups: supported by the National Natural Science Foundation of China (No.10571153)(from 2006 to 2008, RMB$250000)
  7. The method of representations of algebras and the string theory: supported by the National Natural Science Foundation of China (No. 10871170)(from 2009 to 2011, RMB$250000)
  8. Study on some fundamental subjects in the frontier of algebra and combinatorics, supported by the Natural Science Foundation of Zhejiang Province (No. D7080064) (from 2009 to 2011, RMB$250000)



  1.     Li, Fang: Solutions of Yang-Baxter equation in endomorphism semigroups and quasi-(co)braided almost bialgebras. Comm. Algebra, 28(5):2253-2270 (2000)
  2.     Li, Fang and Liu, Zhongkui: A sufficient condition for smash product as a transfinite left free normalizing extension and its application. Acta Math. Sinica (Chinese Series) 42(2): 377-381 (1999); (English Series) 16(1): 71-78(2000)
  3.     Li, Fang: Green's equivalences on coalgebras. Acta Math. Sinica (Chinese), 43(3):399-414(2000)
  4.     Liu, Zhongkui and Li, Fang: On locally Noetherian modules. J. of Math. Research & Exposition 20(4): 491-497 (2000)
  5.     Li, Fang: Weaker structures of Hopf algebras and singular solutions of Yang-Baxter equation, Symposium on The Frontiers of Physics at Millennium, 143-147, World Scientific Publishing Co. Pte. Ltd, Singapore, 2001
  6.     Duplij, Steven and Li, Fang: On regular solutions of Quantum Yang-Baxter equation and weak Hopf algebras. Journal of Kharkov National University, ser. Nuclei, Particles and Fields 521, 15-30 (2001)
  7.     Li, Fang and Tong, Xiao-ping: Amendment and imporovement of some basic
  8.    conclusions in "Hopf Algebra"(E.Abe), Journal of Zhejiang University (Science Edition), 28(5): 473-477 (2001)
  9.     Duplij, Steven and Li, Fang: Regular Solutions of Quantum Yang-Baxter Equation from Weak Hopf algebras, Czechoslovak J. of Physics, 51(12): 1306-1311 (2001)
  10.     Li, Fang: Some weaker structures of Hopf algebras, J. of Zhejiang University (Science), 29(3): 246-254 (2002)
  11.     Li, Fang and Duplij, Steven: Weak Hopf algebras  and singular solutions of Quantum Yang-Baxter equation, Comm. Math. Phys. 225: 191-217 (2002)
  12.     Li, Fang: The right braids, quasi-braided pre-tensor categories and general Yang-Baxter operators, Comm. Algebra, 32(2): 397-441 (2004)
  13.     Wang, Guojun, Li, Fang, Liu, Gngxiang: Advance of Researches on Weaker Structures of Hopf Algebras, Chinese Academic Forum, Vol.10: 28-33 (2004)
  14.     Li, Fang and Trotter, P G: Concise Encyclopaedia of Supersymmetry and Noncom- mutative Structures in Mathematics and Physics, editted by S.Duplij, W.Siegel, J.Bagger, Kluwer Academic Publishers, Dordrecht, 2004, ISBN 1-4020-1338-8, pp.92-93, 97, 209, 502-503
  15.     Li, Fang: On quasi-bicrossed products of weak Hopf algebras, Acta Math. Sinica(English Series), 20(2): 305-318 (2004)
  16.     Li, Fang and Zhang, Yao-zhong: Quantum Doubles From A Class of Noncocom- mutative Weak Hopf Algebras, J. of Math. Physics 45(8): 3266-3281 (2004)
  17.     Li, Fang: Structure theorem of a right Hopf module over a right Hopf algebra,  Algebra Colloquium 11(3): 301-312 (2004)
  18.     Li, Fang: structure of quantum doubles of finite Clifford monoids,  Comm. in Algebra 32(10): 4085-4097 (2004)
  19.     Li, Fang and Chen, Lili: Set-Representation Of A Quiver And Relationship With Linear-Representation, Scientiae Mathematicae Japonicae 62(1):47-56(2005); Online:139-148(e-2005)
  20.     Jia, Ling and Li, Fang: Rudiment of weak Doi-Hopf \pi-modules, J. Zhejiang  Univ. (SCI) 6A(Suppl.I)(2005), 144-154
  21.     Li, Fang and Cao, Haijun: Semilattice graded weak Hopf algebra and its related quantum G-double, Journal of Mathematical Physics 46(8):083519-1~17 (2005)
  22.     Li, Fang and Cao, Haijun: Semilattice graded weak Hopf algebra and its quantum doubles, ADVANCES IN RING THEORY, Proceedings of the 4th China-Japan-Korea International Conference Nanjing, China 24 - 28 June 2004, pp.139-150 edited by J L Chen (Southeast University, China), N Q Ding (Nanjing University, China) & H Marubayashi (Naruto University of Education, Japan), World Scientific, Pub. date: Aug 2005, ISBN 981-256-425-X
  23.     Liu, Gongxiang and Li, Fang: On strongly groupoid graded rings and the corresponding Clifford theorem", Algebra Colloquium 13(2):181-196(2006)
  24.     Shi, Meihua and Li, Fang: The categroy of modules over a triangular matrix ring of order n and its homological characterizations, Acta Math. Sinica (Chinese Series), 49(1): 215-224 (2006)
  25.     Li, Fang and Liu, Gong-xiang: Weak tensor category and related generalized Hopf algebras, Acta Mathematica Sinica (English Series), 22(4): 1027-1046 (2006)
  26.     Zhang, Liangyun and Li, Fang: Cylinder Coalgebras and Cylinder Coproducts for Quasitriangular Hopf Algebras, 数学研究与评论,26(4):635-648(2006)
  27.     Jia, Ling and Li, Fang: Global dimension of weak smash product, J. of Zhejiang University (Science A) 2006, 12(7),2088-2092
  28.     Li, Fang and Zhang Mianmian: Invariant properties of representations under cleft extensions, Science in China (Series A-Mathematics), 2006, 36(12), 1377-1388 (in Chinese); 2007, Vol.50, No.1, pp.121-131 (in English)
  29.     Liu, Gongxiang and Li, Fang: Pointed Hopf algebras of finite representation type and their Classification, Proc. AMS, 135 (2007), 649-657
  30.     贾玲和李方entwined模的Frobenius性质和Maschke型定理,数学学报(中文版),50(1):105-116 (2007)
  31.     Ye, Lixia and Li, Fang: Weak quantum Borcherds superalgebras and their representations, Journal of Mathematical Physics, 2007, 48(2): 023502,pp.16
  32.     Jia, Ling and Li, Fang: On weak group entwined structure, Houston Journal of Mathematics, 33(2): 433-450 (2007)
  33.     Jia Ling and Li Fang: The cohomology group of weak entwining structure,Science in China (Series A-Mathematics), 37(1): 55-63 (2007)
  34.     Qiao, Husheng, Li, Fang: When all S-Posets Are Principally Weakly Flat, Semigroup Forum, 75 (2007), 536–542
  35.     Li, Fang: Characterization of left Artinian algebras through pseudo path algebras, J. of Austr. Math. Soc. 83(2007): 385-416. 
  36.     Qiao, Husheng, Li, Fang: The flatness properties of S-poset A(I) and Rees factor S-posets, Semigroup Forum, 77 (2008), 306–315
  37.     Jia Ling and Li Fang: Hopf代数上的几乎可裂序列,数学学报(中文),20087月,514749-754
  38.     Jia, LingLi, Fang Alternative Doi-Hopf modules over weak Hopf algebras. (Chinese) Acta Math. Sci. Ser. A Chin. Ed. 28 (2008), no. 6, 1067--1076
  39.     Li, Fang, Cao, Haijun and Wang Guojun: A special class of tensor categories initiated by inverse braid monoids, Discrete Mathematics308(2008)4978-4991                                                                           
  40.     Li, Fang and Wen, Daowei: Ordinary quiver, AR-quiver and natural quiver of an algebra, in Geometry, Analysis and Topology of Discrete Groups, 271—304, Advanced Lectures in Mathematics 6, Editors: Lizhen Ji, Kefeng Liu, Lo Yang, Shing-Tung Yau, Higher Education Press & International Press, Beijing, 2008
  41.     Munir Ahmed and Fang Li: The Representation of Clifford Monoids and Semilattice Graded Weak Hopf Algebras: A Motivating Note, Journal of Modern Mathematics and Statistics 2(3): 85-92, 2008
  42.     Wang, Guojun and Li, Fang: On minimal Horse-shoe Lemma, Taiwanese J. of Mathematics, 12 (2008), no. 2, 373--387.
  43.     Li, Fang and Liu, Gong-xiang: Generalized Path Coalgebra And Generalized Dual Gabriel Theorem, Acta Math. Sinica (Chinese Series), 51(5), 2008, 853-862
  44.     Munir Ahmed, Fang LiSelf-Dual Weak Hopf Algebras,Acta Math. Sinica (Series B),Dec., 2008, Vol. 24, No. 12, pp. 1935–1948
  45.     Munir Ahmed and Fang Li: Ore extensions as weak Hopf algebras, The Arabian Journal for Science and Engineering, 33(2C),2008,19-26   (SCI)
  46.     Mianmian Zhang and Fang Li, Representations of skew group algebras induced from ii-modules of path algebras, Journal of Algebra 321 (2009) 567–581
  47.     Dongming Cheng and Fang Li, THE STRUCTURE OF WEAK HOPF ALGEBRAS CORRESPONDING TO Uq(sl2), Communications in Algebra, 37(2009): 729–742
  48.     Chen, Lili and Li, Fang: Dual Hopf algebras from a quiver and dual quiver quantum groups(由箭图构造的对偶Hopf代数和量子群)数学物理学报Acta Mathematica Scientia,2009, 29A(2)505-516
  49.     Jia, LingLi, Fang Doi-Hopf $\pi$-modules and Yetter-Drinfeld $\pi$-modules over a weak $T$-coalgebra. Adv. Math. (China) 38 (2009), no. 1,117—126
  50.     Qiao, HushengLi, Fang On monoids for which all condition $(P)$ acts are strongly flat. Comm. Algebra 37 (2009), no. 1, 234—241
  51.     Ye, Li-xia; Li, Fang, Center and quasi-R-matrix of weak quantum Borcherds superalgebras, Advances in Mathematics (China), 38(2009), no.5, 566-578
  52.     Li, Fang, Chen, Lili: The natural quiver of an artinian algebra, Algebras and representation theory, Published online, 28 November 2009Volume 13, Issue 5 (2010), Page 623--636.
  53.     Jia, Ling and Li, Fang:  Quantum Double for a Weak T–Coalgebra, Algebra Colloquium, 17 : 3 (2010) 475--486
  54.     Wang, Guojun and Li, Fang: The generalized extension closure of Koszul objects, ACTA MATHEMATICA SINICA, Chinese Series, 53(6) 2010: 1065-1074