Shiping Liu



BSc (1982, Changsha), MSc (1985, Changsha & Beijing), PhD (1991, Liverpool)


    Pour me rejoindre To contact me
Département de mathématiques Fax:1-819-821 7189
Université de Sherbrooke 1-819-791 3063 (Maison Home)
Sherbrooke, Québec 1-819-821 8000-62017 (Bureau Office)
Canada J1K 2R1 E-mail: shiping.liu@usherbrooke.ca
Bureau: D3-1033-4


Domaine de recherche Research Area                

Théorie des représentations des algèbres                       Representation Theory of Algebras              


Comité éditorial Editorship
  1. Bulletin of the Malaysia Mathematical Sciences Society.


Liste de publications Publication List
  1. Z. Lin and S. Liu, Auslander-Reiten theory via Nakayama duality in abelian categories, arXiv:2512.19296 (2025).
  2. S. Liu and G. Todorov, Representation theory of hereditary artin algebras of finite representation type, arXiv: 2506.22987 (2025).
  3. A. Bouhada, M. Huang, Z. Lin and S. Liu, A representation theoretic perspective of Koszul theory, arXiv:2411.15449 (2024).
  4. Z. Lin and S. Liu, Representation theory of graded algebras given by locally finite quivers, J. Algebra 683 (2025) 672 - 718.
  5. S. Liu and Y. Yin, Module categories of small radical nilpotency, Algebr. Represent. Theor. 27 (2023) 333 – 361.
  6. S. Liu and H. Niu, Almost split sequences in tri-exact categories, J. Pure Appl. Algebra 226 (2022) 1 - 31.
  7. S. Liu and Jinde Xu, Auslander-Reiten components with bounded short cycles, Comm. Algebra 46 (2018) 1959 - 1970.
  8. R. Bautista and S. Liu, The bounded derived categories of an algebra with radical squared zero, J. Algebra 482 (2017) 303 - 345.
  9. S. Liu and C. Paquette, Cluster categories of type A double infinity and triangulations of the infinite strip, Math. Z. 286 (2017) 197 - 222; see also arXiv: 1505.06062.
  10. S. Liu and C. Paquette, Standard components of a Krull-Schmidt category, Proc. Amer. Math. Soc. 143 (2015) 45 - 59.
  11. S. Liu, Another characterization of tilted algebras, Arch. Math. 104 (2015) 111 - 123.
  12. R. Bautista and S. Liu, Covering theory for linear categories with application to derived categories, J. Algebra 406 (2014) 173 - 225.
  13. S. Liu, Puiman Ng, and C. Paquette, Almost split sequences and approximations, Algebr. Represent. Theor. 16 (2013) 1809 - 1827.
  14. R. Bautista, S. Liu, and C. Paquette, Representation theory of strongly locally finite quivers, Proc. London Math. Soc. 106 (2013) 97 - 162.
  15. C. Chaio and S. Liu, A note on the radical of a module category, Comm. Algebra 41 (2013) 4419 - 4424.
  16. K. Igusa, S. Liu, and C. Paquette, A proof of the strong no loop conjecture, Adv. Math. 228 (2011) 2731 - 2742.
  17. S. Liu, Auslander-Reiten theory in a Krull-Schmidt category, Sao Paulo J. Math. Sci. 4 (2010) 425 - 472.
  18. S. Liu and C. Paquette, Stably triangulated algebras, J. Algebra 320 (2008) 2629 - 2631.
  19. S. Liu and C. Paquette, Some homological conjectures for quasi-stratified algebras, J. Algebra 301 (2006) 240 - 255.
  20. S. Liu and J.-P. Morin, The strong no loop conjecture for special biserial algebras, Proc. Amer. Math. Soc. 132 (2004) 3513 - 3523.
  21. R.-O. Buchweitz and S. Liu, Hochschild cohomology and representation-finite algebras, Proc. London Math. Soc. (3) 88 (2004) 355 - 380.
  22. R.-O. Buchweitz and S. Liu, Dimension of the mesh algebra of a finite Auslander-Reiten quiver, Comm. Algebra (5) 31 (2003) 2207 - 2217.
  23. S. Liu, Preprojective modules and Auslander-Reiten components, Comm. Algebra (12) 31 (2003) 6051 - 6061.
  24. R.-O. Buchweitz and S. Liu, Artin algebras with loops but no outer derivations, Algebr. Represent. Theor. 5 (2002) 149 - 162.
  25. S. Liu, Almost regular Auslander-Reiten components and quasitilted algebras, Comm. Algebra (2) 29 (2001) 687 - 679.
  26. I. Assem, S. Liu, and J. A. de la Pena, "The strong simple connectedness of a tame tilted algebra", Comm. Algebra 28 (2000) 1553 - 1565 (Review).
  27. F. Huard and S. Liu, Tilted string algebras, J. Pure Appl. Algebra 153 (2000) 151 - 164.
  28. F. Huard and S. Liu, Tilted special biserial algebras, J. Algebra 217 (1999) 679 - 700.
  29. I. Assem and S. Liu, "Strongly simply connected algebras", J. Algebra 207 (1998) 449 - 477 (Review).
  30. I. Assem and S. Liu, "Strongly simply connected tilted algebras", Ann. Sci. Math. Quebec 21 (1997) 13 - 22 (Review).
  31. S. Liu, Shapes of connected components of the Auslander-Reiten quivers of artin algebras, Canad. Math. Soc. Conf. Proc. 19 (1995) 109 - 137.
  32. S. Liu, "On short cycles in a module category", J. London Math. Soc. 51 (1995) 62 - 74 (Review).
  33. S. Liu and R. Schultz, "The existence of bounded infinite DTr-orbits", Proc. Amer. Math. Soc. 122 (1994) 1003 - 1005 (Review).
  34. S. Liu, "Infinite radicals in standard Auslander-Reiten components", J. Algebra (2) 166 (1994) 245 - 254 (Review).
  35. D. Happel and S. Liu, "Module categories without short cycles are of finite type", Proc. Amer. Math. Soc. 120 (1994) 371 - 375 (Review).
  36. S. Liu, "Almost split sequences for non-regular modules", Fund. Math. 143 (1993) 183 - 190 (Review).
  37. S. Liu, "Tilted algebras and generalized standard Auslander-Reiten components", Arch. Math. 61 (1993) 12 - 19 (Review).
  38. S. Liu, "The connected components of the Auslander-Reiten quiver of a tilted algebra", J. Algebra 161 (1993) 505 - 523 (Review).
  39. S. Liu, "Semi-stable components of an Auslander-Reiten quiver", J. London Math. Soc. (2) 47 (1993) 405 - 416 (Review).
  40. S. Liu, "The degrees of irreducible maps and the shapes of Auslander-Reiten quivers", J. London Math. Soc. (2) 45 (1992) 32 - 54 (Review).
  41. S. Liu, "The termination problem for the extension construction of lower radical classes", (Chinese) J. Math. Wuhan 7 (1987) 379 - 384 (Review).
  42. S. Liu, "The BM-structure of M-rings", (Chinese) J. Hunan Normal University (Science series) 9 (1986) 7 - 10 (Review).
  43. S. Liu, "The structure of 2-primitive near-rings and the semi-groups of endomorphisms of their additive groups", (Chinese) J. Hunan Normal University (Science series) 4 ( 1984 ) 1 - 8 (Review).
  44. S. Liu, "A necessary and sufficient condition for an associative ring to be a direct sum of division rings", (Chinese) J. Hunan Normal University (Science series) 2 (1984) 14 - 16 (Review).


Exposés Talks
  1. Module categories of small radical nilpotency, Advances in Representation Theory of Algebras IX; June 12 - 16, 2023 (Kingston, Ontario).
  2. The radical nipotency of the module category of a hereditary algebra of Dynkin type, Maurice Auslander International Conference; April 26 - May 1, 2023 (Woods Hole, MA, USA).
  3. Module categories with a null forth power of the radical, The Winter Meeting of the Canadian Mathematical Society; December 2 - 5, 2022 (Toronto, Ontario).
  4. Auslander-Reiten theory in tri-exact categories, Maurice Auslander International Conference; October 26 - 30, 2022 (Woods Hole, MA, USA).
  5. Almost split sequences in tri-exact categories, Advances in Representation Theory of Algebras VIII; September 19 - 23, 2022 (Torun, Poland).
  6. Koszul duality for non-graded derived categories, Advances in Representation Theory of Algebras VII; May 17 - 28, 2021 (Online, RMC, Canada).
  7. Geometric properties of matrices, Lecture at Shaoxing University; July 4, 2019(Shaoxing, China).
  8. Homology theory of double complexe with application to Koszul duality, Algebra Seminar at Hunan Normal University; July 2, 2019(Changsha, China).
  9. Koszul duality for non-graded derived categories, Algebra Forum; June 21 - 23, 2019 (Changshu, China).
  10. The Auslander-Reiten theory through triangulated categories, The Summer Meeting of the Canadian Mathematical Society; June 2 - 3, 2018 (Fredericton, New Brunswick).
  11. The derived Auslander-Reiten components of an algebra with radical squared zero, Advances in Representation Theory of Algebras VI; September 4 - 8, 2017 (Luminy, France).
  12. The Auslander-Reiten components with bounded short cycles, Mathematical Congress of the Americas 2017; July 24 - 27, 2017 (Montreal, Canada).
  13. Covering theory and cluster categories, International Workshop on Cluster Algebras and Related Topics; July 10 - 13, 2017 (Tianjin, China).
  14. Cluster categories of type A double inifnity and triangulations of the infinite strip, Seminar at Qing Hua University; June 13, 2016 (Beijing, China).
  15. Linear categories: from module categories to derived categories and cluster categories, The 14th National Conference on Algebra of China; May 26 - 31, 2016 (Yangzhou, China).
  16. Triangulated categories with an infinite cluster structure, Advances in Representation Theory of Algebras V; March 14 - 16, 2016 (Mar Del Plata, Argentina).
  17. Homological dimensions of simple modules over artinian rings, China-Japan-Korea International Conference on Ring Theory VII; July 1 - 6, 2015 (Hangzhou, China).
  18. Another characterization of tilted algebras, Advances in Representation Theory of Algebras IV; June 21 - 26, 2015 (Guanajuato, Mexico).
  19. The bounded derived category of an algebra with radical squared zero, Advances in Representation Theory of Algebras III; June 16 - 20, 2014 (Montreal, Canada).
  20. Covering theory for linear categories with application to derived categories, Advances in Representation Theory of Algebras II; September 9 - 13, 2013 (Torun, Poland).
  21. Standard Auslander-Reiten components and cluster structure of infinite Dynkin type, Algebra Seminar; July 18, 2013 (Tsinghua University, Beijing, China).
  22. Oriented cycles and global dimension of algebras, Algebra Seminar; July 11, 2013 (Hunan Normal University, Changsha, China).
  23. Standard Auslander-Reiten components of a Krull-Schmidt category, Maurice Auslander International Conference; April 18 - 23, 2013 (Woods Hole, MA, USA).
  24. Representation theory of strongly locally finite quivers, Advances in Representation Theory of Algebras I; December 3 - 7, 2012 (CIMAT, Guanajuato, Mexico).
  25. Oriented cycles and the global dimension of an algebra, Seminaire d'Algebre et Geometrie Gradue; November 30, 2012 (Université Laval, Quebec).
  26. Almost split sequences and approximations, Maurice Auslander International Conference; April 25 - 30, 2012 (Woods Hole, MA, USA).
  27. On the global dimension of an algebra, Interactions between Commutative Algebra and Representation Theory; April 13 - 15, 2012 (Syracuse, USA).
  28. Represnetation theory of an infinite quiver, Shanghai International Conference on Representation Theory of Algebras; October 2 - 7, 2011 (Shanghai, China)


Notes de cours Lecture Notes
  1. MAT153: Introduction à l'algèbre linéaire (I)
  2. MAT199: Algèbre linéaire appliquée en informatique
  3. MAT253: Introduction à l'algèbre linéaire (II)
  4. MAT504: Algèbre appliquée
  5. MAT541: Modules et matrices
  6. MAT641: Théorie des corps
  7. MAT721: Algèbre non commutative
  8. MAT729: Algèbre commutative et géométrie algèbre
  9. MAT731: Groupes et représentations des groupes
  10. école d'été: Revétements galoisiens de catégories linéaires


Thèses Supervisées Supervised Theses
  1. Charles Paquette, Algèbres quasi-stratifiées (M.Sc, 2006)
  2. Charles Paquette, Conjectures homologiques, catégories stables et représentations de carquois infinis (Ph.D, 2010)
  3. Hongwei Niu, Auslander-Reiten theory in triangulated categories (M.Sc, 2014)
  4. Hongwei Niu, Constructing Cluster-tilting Subcategories of Cluster Categories of Types A infinity and A double infinity (Ph.D, 2018)
  5. Saliou Lo, Algèbres de dimension finie dont le carré du radical de la catégorie des modules est nul (M.Sc, 2021)
  6. Sogol Damavandi, Nakayama algebras whose module category is radical cubed zero (M.Sc, 2023)
  7. Esha Gupta, Auslander-Reiten theory and string modules in the locally finite-dimensional setting (M.Sc, 2024)
  8. Zetao Lin, The Representation Theory of Graded Algebras and Koszul Algebras (Ph.D, 2024)


Bibliothèque Library
  1. Henri Cartant and Samuel Eilenberg, Homological Algebra, (Princeton University Press, Princeton, 1956).
  2. Lidia Angeleri Hügel, Dieter Happel and Henning Krause Handbook of Tilting Theory, London Mathematical Society Lecture Note Series 332 (Cambridge University Press, Cambridge, 2007).
  3. Hideyuki Matsumura, Commutative Ring Theory, translated by M. Reid (Cambridge University Press, Cambridge, 1986).
  4. Dragan Milicic, Lecture Notes on Derived Categories, preprint.
  5. Amnon Neeman, Triangulated Categories, Annals of Mathematics Studies 148 (Princeton University Press, Princeton, 2001).
  6. Stacks Project, Encyclopaedia of Algebra, preprint.