Présentation

Sujets de recherche

Algèbre.

Disciplines de recherche

Mathématiques fondamentales.

Mots-clés

Catégories amassées, Catégories triangulées, Propriétés homologiques des algèbres, Représentations des algèbres et des carquois, Théorie d'Auslander-Reiten.

Intérêts de recherche

La théorie des représentations des algèbres d'Artin, représentations des carquois infinis, catégories triangulées, algèbre homologique, la théorie d'Auslander-Reiten, co-homologie de Hoschchild, catégories amassées, catégories amassées.

Langues parlées et écrites

Anglais, Français, Mandarin

Publications

Articles de revue

• Shiping Liu. (2015). Another characterization of tilted algebras. Archiv der Mathematik, 104, 111 - 123. (Article publié).
• Shiping Liu, Charles Paquette. (2015). Standard components of a Krull-Schmidt category. Proceedings of the American Mathematical Society, 143, 45 - 59. (Article publié).
• Raymundo Bautista, Shiping Liu. (2014). Covering theory of linear categories with application to derived categories. Journal of Algebra, 406, 173 - 225. (Article publié).
• Shiping Liu, Puiman Ng, Charles Paquette. (2013). Almost split sequences and approximations. Algebras and Representation Theory, 16, 1809 - 1827. (Article publié).
• Claudia Chaio,Shiping Liu. (2013). A note on the radical of a module category. Communications in Algebra, 41, 4419 - 4424. (Article publié).
• Raymundo Bautista, Shiping Liu, Charles Paquette. (2012). Representation theory of strongly locally finite quivers. Proceedings of the London Mathematical Society, 106, 97 - 162. (Article publié).
• Kiyoshi Igusa, Shiping Liu, Charles Paquette. (2011). A proof of the strong no loop conjecture. Advances in Mathematics, 228(5), 2731 - 2742. (Article publié).
• Shiping Liu. (2010). Auslander-Reiten theory in a Krull-Schmidt category. The São Paulo Journal of Mathematical Sciences, 4, 425 - 472. (Article publié).
• Shiping Liu, Charles Paquette. (2008). Stably triangulated algebras. Journal of Algebra, 320(6), 2629 - 2631. (Article publié).
• Shiping Liu, Charles Paquette. (2006). Some homological conjectures for quasi-stratified algebras. Journal of Algebra, 301(1), 240 - 255. (Article publié).
• Shiping Liu, Jean-Philippe Morin. (2004). The strong no loop conjecture for special biserial algebras. Proceedings of the American Mathematical Society, 132(2), 3513 - 3523. (Article publié).
• Ragnar-Olaf Buchweitz, Shiping Liu. (2004). Hochschild cohomology and representation-finite algebras. Proceedings of the London Mathematical Society, 88, 355 - 380. (Article publié).
• Shiping Liu. (2003). Preprojective modules and Auslander-Reiten components. Communications in Algebra, 31(12), 6051 - 6061. (Article publié).
• Ragnar-Olaf Buchweitz, Shiping Liu. (2003). Dimension of the mesh algebra of a finite Auslander-Reiten quiver. Communications in Algebra, 31(5), 2207 - 2217. (Article publié).
• Ragnar-Olaf Buchweitz, Shiping Liu. (2002). Artin algebras with loops but no outer derivations. Algebras and Representation Theory, 5, 149 - 162. (Article publié).
• Shiping Liu. (2001). Almost regular Auslander-Reiten components and quasi-tilted algebras. Communications in Algebra, 29(2), 687 - 679. (Article publié).
• François Huard, Shiping Liu. (2000). Tilted string algebras. Journal of Pure and Applied Algebra, 153, 151 - 164. (Article publié).
• Ibrahim Assem, Shiping Liu, José Antonio de la Pena. (2000). The strong simple connectedness of a tame tilted algebra. Communications in Algebra, 28(3), 1553 - 1565. (Article publié).
• François Huard, Shiping Liu. (1999). Tilted special biserial algebras. Journal of Algebra, 217(2), 679 - 700. (Article publié).
• Ibrahim Assem, Shiping Liu. (1998). Strongly simply connected algebras. Journal of Algebra, 207(2), 449 - 477. (Article publié).
• Ibrahim Assem, Shiping Liu. (1997). Strongly simply connected tilted algebras. Annales mathématiques du Québec, 21, 13 - 22. (Article publié).
• Shiping Liu. (1995). Shapes of connected components of the Auslander-Reiten quivers of artin algebras. Canada Mathematical Society Conference Proceedings, 19, 109 - 137. (Article publié).
• Shiping Liu. (1995). On short cycles in a module category. Journal of the London Mathematical Society, 51(1), 62 - 74. (Article publié).
• Shiping Liu, Rainer Schultz. (1994). The existence of bounded infinite DTr-orbits. Proceedings of the American Mathematical Society, 122(4), 1003 - 1005. (Article publié).
• Shiping Liu. (1994). Infinite radicals in standard Auslander-Reiten components. Journal of Algebra, 166(2), 245 - 254. (Article publié).
• Dieter Happel, Shiping Liu. (1994). Module categories without short cycles are of finite type. Proceedings of the American Mathematical Society, 120(2), 371 - 375. (Article publié).
• Shiping Liu. (1993). Almost split sequences for non-regular modules. FUNDAMENTA MATHEMATICAE, 143, 183 - 190. (Article publié).
• Shiping Liu. (1993). The connected components of the Auslander-Reiten quiver of a tilted algebra. Journal of Algebra, 161(2), 505 - 523. (Article publié).
• Shiping Liu. (1993). Tilted algebras and generalized standard Auslander-Reiten components. Archiv der Mathematik, 61(1), 12 - 19. (Article publié).
• Shiping Liu. (1993). Semi-stable components of an Auslander-Reiten quiver. Journal of the London Mathematical Society, 47(3), 405 - 416. (Article publié).
• Shiping Liu. (1992). The degrees of irreducible maps and the shapes of Auslander-Reiten quivers. Journal of the London Mathematical Society, 45(1), 32 - 54. (Article publié).
• Shiping Liu. (1987). The termination problem for the extension construction of lower radical classes. J. Math. (Wuhan), 7, 379 - 384.
• Shiping Liu. (1986). The BM-structure of M-rings. J. Hunan Normal University (Sci. Series), 9, 32 - 54. (Article publié).
• Shiping Liu. (1984). A necessary and sufficient condition for an associative ring to be a direct product of division rings. J. Hunan Normal University (Sci. Series), 2, 14 - 16. (Article publié).
• Shiping Liu. (1984). The structure of 2-primitive near-rings and the semi-groups of endomorphisms of their additive groups. J. Hunan Normal University (Sci. Series), 4, 1 - 8. (Article publié).
• Shiping Liu, Charles Paquette. Cluster categories of type A double infinity and triangulations of the infinite strip. (Article soumis).

Autres contributions

Présentations

• (2015). Homological dimensions of simple modules over artinian rings. The Seventh China-Japan-Korea International Conference on Ring Theory. Hangzhou.
• (2015). Another characterization of tilted algebras. Advances in Representation Theory of Algebras IV. Guanajuato.
• (2014). The bounded derived category of an algebra with radical squared zero. Advances in Representation Theory of Algebras III. Montreal.
• (2013). Covering theory for linear categories with application to derived categories. Advances in Representation Theory of Algebras II. Torun.
• (2013). Standard Auslander-Reiten components of a Krull-Schmidt category. Maurice Auslander Distinguished Lectures and International Conference. Woods Hole.
• (2012). Representation theory of strongly locally finite quivers. Advances in Representation Theory of Algebras I. Guanajuato.
• (2012). Almost split sequences and approximations. Maurice Auslander Distinguished Lectures and International Conference. Woods Hole.
• (2012). On the global dimension of an algebra. Interactions between Commutative Algebra and Representation Theory. Syracuse.
• (2011). Representation theory of an infinite quiver. Shanghai International Conference on Representation Theory of Algebras. Shanghai.