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Koszul algebras and finite Galois coverings

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Abstract

The relationships between Koszulity and finite Galois coverings are obtained, which provide a construction of Koszul algebras by finite Galois coverings.

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References

  1. Beilinson A A, Ginzburg V A, Soergel W. Koszul duality patterns in representation theory. J Amer Math Soc, 9: 473–527 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Green E L, Martínez-Villa R. Koszul and Yoneda algebras II. In: Representation theory of algebras, CMS Conf Proc, Vol 24. Providence: Amer Math Soc, 1998, 227–244

    Google Scholar 

  3. Butler M C R, King A D. Minimal resolutions of algebras. J Algebra, 121: 323–362 (1999)

    Article  MathSciNet  Google Scholar 

  4. Green E L, Hartman G, Marcos E N, Solberg Ø. Resolutions over Koszul algebras. Arch Math (Basel), 85: 118–127 (2005)

    MATH  MathSciNet  Google Scholar 

  5. Martínez-Villa R. Applications of Koszul algebras: The preprojective algebras. In: Representation theory of algebras, CMS Conf Proc, Vol 18, Providence: Amer Math Soc, 1996, 487–504

    Google Scholar 

  6. Green E L, Martínez-Villa R. Koszul and Yoneda algebras. In: Representation theory of algebras, CMS Conf Proc, Vol 18. Providence: Amer Math Soc, 1996, 247–297

    Google Scholar 

  7. Green E L. Introduction to Koszul algebras. In: Representation theory and algebraic geometry, London Math Soc Lecture Note Ser, Vol 238. Cambridge: Cambridge University Press, 1997, 45–62

    Google Scholar 

  8. Anderson F W, Fuller K R. Rings and categories of modules. Grad Texts in Math, Vol 13. Berlin: Springer-Verlag, 1974

    Google Scholar 

  9. Martínez-Villa R. Serre duality for generalized Auslander regular algebras. In: Trends in the representation theory of finite-dimensional algebras, Contemp Math, Vol 229. Providence: Amer Math Soc, 1996, 237–263

    Google Scholar 

  10. Cohen M, Montgomery S. Group-graded rings, smash products, and group actions. Trans Amer Math Soc, 282: 237–258 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  11. Martínez-Villa R. Skew group algebras and their Yoneda algebras. Math J Okayama Univ, 43: 1–16 (2001)

    MATH  MathSciNet  Google Scholar 

  12. Auslander M, Reiten I, Smalø S O. Galois actions on rings and finite Galois coverings. Math Scand, 65: 5–32 (1989)

    MATH  MathSciNet  Google Scholar 

  13. Green E L. Graphs with relations, covering and group-graded algebras. Trans Amer Math Soc, 279: 297–310 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  14. Auslander M, Reiten I, Smalø S O. Representation theory of artin algebras. Cambridge studies in advancedmathematics, Vol 36, Cambridge: Cambridge university press, 1995

    Google Scholar 

  15. Bongartz K, Gabriel P. Covering spaces in representation-theory. Invent Math, 65: 331–378 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  16. Gabriel P. The universal cover of a representation-finite algebra. In: Representations of algebras, Lecture Notes in Math, Vol 903. Berlin: Springer-Verlag, 1981, 68–105

    Chapter  Google Scholar 

  17. Ringel C M. The preprojective algebra of a quiver. In: Representation theory of algebras, CMS Conf Proc, Vol 24. Providence: Amer Math Soc, 1998, 467–480

    Google Scholar 

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Authors and Affiliations

  1. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    DeKe Zhao & Yang Han

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  1. DeKe Zhao
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  2. Yang Han
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Correspondence to Yang Han.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10731070)

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Zhao, D., Han, Y. Koszul algebras and finite Galois coverings. Sci. China Ser. A-Math. 52, 2145–2153 (2009). https://doi.org/10.1007/s11425-009-0082-y

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  • DOI: https://doi.org/10.1007/s11425-009-0082-y

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