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Communications in Algebra Volume 51, 2023 - Issue 8
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Research Article

Stability conditions and derived Hall algebras

Xintian Wanga China University of Mining and Technology (Beijing), Beijing, ChinaView further author information
&
Qinghua Chenb School of Mathematics and Statistics, Fu Zhou University, Fu Zhou, Fujian, ChinaCorrespondence[email protected]
View further author information
Pages 3464-3480 | Received 29 Jun 2022, Accepted 19 Feb 2023, Published online: 11 Mar 2023

References

  • Assem, I., Simson, D., Skowronski, A. (2006). Elements of the Representation Theory of Associative Algebras, London Mathematical Society Student Texts 65, Vol. 1. Cambridge: Cambridge University Press.
  • Bridgeland, T. (2007). Stability conditions on triangulated categories. Ann. Math. 166:317–345.
  • Dlab, V., Ringel, C. M. (1976). Indecomposable Representations of Graphs and Algebras. Memoirs of the American Mathematical Society, 6. Providence: American Mathematical Society.
  • Gorodentsev, A. L., Kuleshov, S. A., Rudakov, A. N. (2004). t-stabilities and t-structures on triangulated categories, Izv. Ross. Akad. Nauk Ser. Mat. 68:117–150; translation in Izv. Math. 68:749–781.
  • Guo, J., Peng, L. (1997). Universal PBW-basis of Hall–Ringel algebras and Hall polynomials. J. Algebra 198:339–351.
  • Happel, D. (1988). Triangulated Categories in the Representation Theory of Finite Dimensional Algebras, London Mathematical Society, Lecture Notes Series, Vol. 119, Cambridge: Cambridge University Press.
  • Hille, L., Pena, J. A. D. L. (2002). Stable representations of quivers. J. Pure Appl. Algebra. 172:205–224.
  • Joyce, D. (2008). Configurations in abelian categories. IV. Invariants and changing stability conditions. Adv. Math. 217:125–204.
  • Reineke, M. (2003). The Harder–Narasimham system in quantum groups and cohomology of quiver moduli. Invent. Math. 152:349–368.
  • Ringel, C. M. (1988). Hall algebras. In: Balcerzyk, S., et al., ed. Topics in Algebra, Part 1, Vol. 26. Warsaw: Banach Center Publications, pp. 433–447.
  • Ringel, C. M. (1996). PBW-bases of quantum groups. J. Reine Angew. Math. 470:51–88.
  • Töen, B. (2006). Derived Hall algebras. Duke Math. J. 135:587–615.
  • Wang, X. (2017). On the slopes of semistable representations of tame quivers. Commun. Algebra 45:4809–4816.
  • Xiao, J., Xu, F. (2008). Hall algebras associated to triangulated categories. Duke Math. J. 143:357–373.
  • Zhang, P., Zhang, S. (1998). Indecomposables as elements in affine composition algebras. J. Algebra 210:614–629.
  • Zhang, P. (2000). PBW-basis for the composition algebra of the Kronecker algebra. J. Reine. Angew. Math. 527: 97–116.

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