PERSONAL  INFORMATION

Fang Li, Professor of Department of Mathematics, Zhejiang University

 

ACADEMIC DEGREES

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

 

RESEARCHING AREAS

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

semigroups and their representations, Matrix theory

 

PROFESSIONAL BACKGROUND

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

 

 MAIN RESEARCHING PROJECTS

  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)

 

LIST OF PUBLICATIONS

  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: 弱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: 弱Hopf代数上的几乎可裂序列，数学学报（中文），2008年7月，51（4），749-754
  38.     Jia, Ling; Li, 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 Li：Self-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, Ling; Li, 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, Husheng; Li, 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 2009；Volume 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