Ph.D.(Bielefeld,1999), Professor of Mathematics

Department of Mathematical Sciences,

Tsinghua University,

Beijing 100084, P.R.China

Office: Room 1208, Science Building (Math.)

Tel: +86(0)10-62772862

Fax: +86(0)10-62785847


    Chinese version


Brief CV

  • Education:
    • Oct.1997-Mar.1999, Ph.D. student in Falkultaet fuer Mathematik, Universitaet Bielefeld.
      Supervisor: Professor Dr. C.M.Ringel.
    • Sept.1995-Sept.1997, Ph.D. student in Department of Mathematics, Beijing Normal University.
      Supervisor: Professor Shaoxue Liu.
    • Sept.1986-Jul.1989, Graduate student at Department of Mathematics, Jilin Normal University.
    • Sept.1982-Jul.1986, Undergraduate student at Department of Mathematics,Hunan Normal University.
  • Professional background:
  • Conferences:
    • July. 29-Aug. 2, 2003, 8th National conference on Lie algebras, University of Xiamen, Xiamen, China;
      invited talk: On good filtration dimension and finitistic dimension for stratified algebras.
    • Sept.24-Sept.27,2002, Advanced Seminar on Representation theory of Heck algebras and cellular algebras", Beijing Normal University, Beijing, China;
      invited talk: On good filtration dimensions for quasi-hereditary algebras.
    • Aug.29-Sep.3,2002, International Conference on Algebra--A Satellite Conference of ICM2002, Suzhou University, China;
      invited talk: Relations of Grothendieck groups of triangulated categories.
    • April. 16. 2002, Workshop at Antwerpen: Hopf algebras, noncommutative geometry and separable bimodules, Antwerpen, Belgium;
      invited talk: Separable bimodules and approximations.
    • Aug. 21-Sep.1,2000, The Ninth International Conference on the Representation Theory of Algebras, Beijing, China;
      invited talk: On Delta-good module categories arising from hereditary algebras.
    • Oct.10-14, 1999, 7th national comference on algebras, Beijing Normal University;
      invited talk: Relations for Grothendieck Groups of Quasi-Hereditary Algebras.
    • Aug. 31-Sep.4,1998, The 8.5th International Conference on the Representation Theory of Algebras, Bielefeld, Germany;
      the title of talk: Some combinatorial descriptions of coils.
    • Sep.7-Sep.11,1998, Workshop on Infinite dimensional modules, Bielefeld, Germany.


Research Interests

  • Cluster tilting theory, cluster categories and Calabi-Yau categories
  • Cluster algebras and Calabi-Yau algebras
  • Derived categories and triangulated categories.
  • Quasi-hereditary algebras and relatives.
  • Auslander-Reiten Theory.





    Hiroyuki Nakaoka (Kagishima), 1.11.2016--4.11.2016

    Shiping Liu(Sherbrooke),

    Yu Zhou(NTNU)





    Recent Preprints




    45.Cluster subalgebras and cotorsion pairs in Frobenius
    extriangulated categories (with Wen Chang, Panyue Zhou). arXiv:1610.05006


    44. Torsion pairs in finite 2-Calabi-Yau triangulated categories with maximal rigid objects (with Huimin Chang), see arXiv:1608.03734


    43.Triangulated quotient categories revisited (with Panyue Zhou), see arXiv:1608.000297




    42.Cluster automorphism groups and automorphism groups of exchange graphs (with Wen Chang), see arXiv:1506.02029


    41.Cluster automorphism groups of cluster algebras of finite type (with Wen Chang). J. Algebra 447, 49-515, 2016. see arXiv:1506.01950


    40. Ghost tilting objects in triangulated categories (with Wuzhong Yang), see arXiv:1506.00093;Title is changed as "Relative cluster tilting

    objects in triangulated categories". To appear in Trans AMS.


    39. On the automorphism groups of cluster algebras with coefficients (with Wen Chang), Sciences in China (Mathematics), Vol.59(10),

    1919-1936, 2016.arXiv:1506.01942




    38. On rooted cluster morphisms and cluster structures in 2-Calabi-Yau triangulated categories (with Wen Chang),

    J. Algebra 458, 387-421, 2016. See arXiv:1410.5702 .


    37. On cluster-tilting objects in triangulated categories with Serre duality (with Wuzhong Yang and Jie Zhang),

    To appear in Comm Alg. pdf ,Comm Alg 45(1),299-311,2017


    36. On support tau-tilting modules over endomorphism algebras of rigid objects(with Wen Chang and Jie Zhang),

    Acta Sinica Math (New Series), &Vol.31(9), 1508-1516(2015).




    35. Mutation of torsion pairs in triangulated categories and its geometric realization (with Yu Zhou), pdf. See arXiv:1105.3521 .


    Published Papers(1999-):

    34. T-structures and torsion pairs in a 2-Calabi-Yau triangulated category (with Yu Zhou), pdf(2012-12-28), pdf(2013-07-18), Jour. Lond.Math.Soc.89(1),213-234,2014.

    33. Cotorsion pairs in the cluster category of a marked surface (with Jie Zhang, Yu Zhou), pdf (2012-04-29).pdf(2013-07-05), J. Algebra.391,209-226,2013.


    32. Triangulated quotient categories (With Yu Liu), pdf, pdf(2013-06), Comm. Alg.41(10),3720-3738,2013.. See also arXiv:1024.2024 .


    31.Cluster algebras of type C via cluster tubes (with Yu Zhou), pdf, title changed as "Cluster algebras arising

    from cluster tubes".See also arXiv:1008.3444. Jour Lond.Math.Soc.89(3),703-723, 2014.


    30. Finite repetitive generalized cluster complexes and d-cluster categories (with Teng Zou), pdf. Algebra Colloquium, 20 (1), 123-140,2013.


    29. Maximal rigid subcategories in 2-Calabi-Yau triangulated categories (with Yu Zhou), pdf(2011-9) . Journal of Algebra 348, 49-60, 2011. See also arXiv:1004.5475.


    28.Cluster-tilted algebras and their intermediate coverings, pdf . Communications in Algebra, 39,2437-2448.2011. See also arXiv:0808.2352.


    27. Cluster combinatorics of d-cluster categories (with Yu Zhou), dvi . Journal of Algebra, 321, 2898-2915,2009. See also arXiv:arXiv:0712.1381.


    26.d-Cluster tiltings in d-cluster categories and their combinatorics (with Yu Zhou ), Oberwolfach Report Vol. 5(1), 453-454, 2008.


    25. From triangulated categories to abelian categories --- cluster tilting in a general framework} (with S. Koenig ), dvi, appeared in Math.Zeit. 258(1), 143-160, 2008.. See also arXiv: math.RT/0605100.


    24.Generalized Cluster Complexes via Quiver Representations, dvi, 2006. Appeared in Journal of Algebraic Combinatorics 27, 25-54, 2008. See also arXiv: math.RT/0607155.


    23. Preprojective cluster variables of acyclic cluster algebras, dvi. Comm Algebra. 35. 2857-2871, 2007. see also arXiv:     math.RT/0511706.


    22. Applications of BGP-reflection functors: isomorphisms of cluster algebras, dvi Sciences in China (Mathematics), Vol.49(12), 1839-1854, 2006.  


    21. Tilting theory in cluster categories of hereditary abelian categories, dvi. Appeared in Journal of Algebra, Vol.304, 832-850,2006 with a new title "Equivalences between cluster categories. See also arXiv: math.RT/0511382.


    20. BGP-reflection functors and cluster combinatorics, pdf, 2004. Journal of pure and applied algebra, Vol.209, 497-506, 2007. See also arXiv: math.RT/0511380.


    19. Separable bimodules and approximations (with S. Caenepeel ), ps, 2002. Algebras and Representation Theory, Vol.8, 207-223, 2005.


    18. Locally finite triangulated categories (with J.Xiao), pdf, 2003. Journal of Algebra, 290, 473-490,2005.


    17. BGP-reflection functors in root categories (with J.Xiao and Guanglian Zhang),dvi. Sciences in China (Mathematics), Vol.48(8), 1033-1045, 2005.


    16. On characteristic modules of quasi-hereditary graded algebras, dvi, Communications in Algebra. Vol. 32, 2919- 2928, 2004.


    15. Finitistic dimension and good filtration dimensions of stratified algebras (with S.G.Wang). Bulletin of Australian Mathematical society, Vol.69, 341-347, 2004.


    14.On Delta-good filtration dimensions of standardly stratified algebras (with S. Caenepeel ) pdf. Communications in Algebra. Vol.32, 1603-1614, 2004.


    13. The structure of gr-simple rings, ps, dvi. Northeast Math. J. Vol.19(3), 231-234. (2003).


    12.Relative Approximations and Maschke Functors, pdf. Bulletin of Australian Mathematical society, Vol.67, 219-224(2003).


    11.A condition for a translation quiver to be a coil (with Zongyi Hu). Acta Sinica Math (New Series), Vol.19(1), 107-126(2003).


    10.Relations for Grothendieck Groups of Triangulated categories (with Jie Xiao), pdf. Journal of Algebra, Vol.257, 37-50(2002).


    9.On Delta-good module categories arising from hereditary algebras. Communications in Algebra, Vol.29(12), 5575-5588(2001).


    8.Contravariantly finite subcategories and adjunctions, dvi. Algebra Colloquium, Vol.8(3),307-314(2001).


    7.Contravariantly finite subcategories in a tilting torsion class. Progress in Nature Sciences, Vol.11(10),797-800 (2001).


    6.Triangular matrix algebras over quasi-hereditary algebras. Tsukuba Journal of Mathematics, Vol.25(1),1-11(2001).


    5. A criterion for coils, pdf,. Communications in Algebra, Vol.29(1), 253-269(2001).


    4.Coils for vectorspace categories, pdf,. Communications in Algebra, Vol.29(3), 1191-1214 (2001).


    3.On Delta-good module categories without short cycles (with Bangming Deng). Proc. Amer. Math. Soc., Vol.129(1), 69-77(2001).


    2.Relations for Grothendieck Groups of Quasi-hereditary algebras. Chinese Journal of Contemporary Mathematics Vol.22(2),119-124(2001), A Chinese version appeared in Chin. Ann. of Math (A), Vol.22(2), 135-140(2001).


    1.Smash Products of Quasi-hereditary Graded Algebras, pdf. Archive der Mathematik, Vol.72(6), 433-437 (1999)








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