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Communications in Algebra Volume 46, 2018 - Issue 11
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Articles

Canonical decomposition and quiver representations over finite field

Qinghua ChenCollege of Mathematics and computer Science, Fu Zhou University, Fu Zhou, Fujian, ChinaCorrespondence[email protected]
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Ye LiuSchool of Mathematical Sciences, Beijing Normal University, Beijing, China;The high school attached to Hunan Normal University, Chang Sha, Hunan, ChinaView further author information
Pages 4859-4867 | Received 12 Aug 2016, Published online: 23 Apr 2018

References

  • Chen, Q., Liu, Y. Canonical decomposition and quiver representations of type Ãn over finite field, preprint.
  • Crawley-Boevey, W. W., Van den Bergh, W. (2001). Absolutely indecomposable representations and Kac-Moody Lie algebras, With a appendix by Hiruku Nakajima. Invent. Math. (3) 155:537–559.
  • Deng, B., Du, J., Parshall, B., Wang, J. (2008). Finite dimensional algebras and Quantum Groups, Mathematical Surveys and Monographs, Vol. 150. Providence, RI: American Mathematical Society.
  • Derksen, H., Weyman, J. (2002). On the canonical decomposition of quiver representations. Compos. Math. 133:245–265.
  • Derksen, H., Weyman, J. (2006). Combinatorics of quiver representations. Ann. Inst. Four. 61(3):1061–1131.
  • Dlab, V., Ringel, C. M. (1976). Indecomposable representations of graphs and algebras. Mem. Am. Math. Sco. 173: 1–57.
  • Gabriel, P. (1972). Unzerlegbare Darstellungen I. Manuscr. Math. 6:71–103.
  • Gabriel, P., Roiter, A. V. (1992). Representations of finite-dimensional algebras. In: Keller, B., ed. Encyclopaedia of Mathematical Sciences, 73, Algebra, Vol. VIII. Berlin: Springer.
  • Hausel, T. (2010). Kac conjecture from Nakajima quiver varieties. Invent. Math 1:21–37.
  • Hua, J. (2000). Counting representations of quivers over finite fields. J. Algebra 226:1011–1013.
  • Kac, V. (1980). Infinite root systems, representations of graphs and invariant theory. Invent. Math. 56:57–92.
  • Kac, V. (1982). Infinite root systems, representations of graphs and invariant theory II. J. Algebra 78:141–162.
  • Kac, V. (1983). Root Systems, Representations of Quivers and Invariant Theory, Lecture Notes in Mathematics, Vol. 996. Berlin: Springer, pp. 74–108.
  • Schofield, A. (1992). General representations of quivers. Proc. London Math. Soc. (3) 65:46–64.
  • Schofield, A. (2001). Birational classification of moduli spaces of representations of quivers, Indagat. Math. (3) 12:407–432.
  • Stanley, R. P. (997). Enumerative Combinatorics I. Cambridge: Cambridge University Press.
  • Zhang, P., Zhang, Y., Guo, J. (2001). Minimal generators of Ringel-Hall algebras of affine quivers. J. Algebra 239:675–704.

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