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(s, t, d)-bi-Koszul algebras

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Abstract

The paper focuses on the 1-generated positively graded algebras with non-pure resolutions and mainly discusses a new kind of algebras called (s, t, d)-bi-Koszul algebras as the generalization of bi-Koszul algebras. An (s, t, d)-bi-Koszul algebra can be obtained from two periodic algebras with pure resolutions. The generation of the Koszul dual of an (s, t, d)-bi-Koszul algebra is discussed. Based on it, the notion of strongly (s, t, d)-bi-Koszul algebras is raised and their homological properties are further discussed.

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References

  1. Backelin J, Froberg R. Koszul algebras, Veronese subrings and rings with linear resolutions. Rev Roumaine Math Pures Appl, 30: 85–97 (1985)

    MATH  MathSciNet  Google Scholar 

  2. Berger R. Koszulity of nonquadratic algebras. J Algebra, 239: 705–734 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Brenner S, Butler M C R, King A D. Periodic algebras which are almost Koszul. Algebra Rep Theory, 5: 331–367 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. Green E L, Marcos E N, Martinez-Villa R, et al. D-Koszul algebras. J Pure Appl Algebra, 193: 141–162 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Lü J F, He J W, Lu D M. Piecewise-Koszul algebras. Sci China Ser A, 50: 1795–1804 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Polishchuk A, Positselski L. Quadratic algebras. In: University Lecture Series, Vol. 37. Providence, RI: American Mathematical Society, 2005

    Google Scholar 

  7. Lu D M, Si J R. Koszulity of algebras with non-pure resolutions. Comm Algebra, (in press)

  8. Green E L, Marcos E. δ-Koszul algebras. Comm Algebra, 33: 1753–1764 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Green E L, Snashall N. Finite generation of Ext for a generalization of D-Koszul algebras. J Algebra, 295: 458–472 (2006)

    MATH  MathSciNet  Google Scholar 

  10. Lu D M, Palmieri J H, Wu Q S, et al. Regular algebras of dimension 4 and their A ∞-Ext-algebras. Duke Math J, 137(3): 647–671 (2007)

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Dianzi University, Hangzhou, 310018, China

    JunRu Si

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  1. JunRu Si
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Correspondence to JunRu Si.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10571152) and the Natural Science Foundation of Zhejiang Province of China (Grant No. J20080154)

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Si, J. (s, t, d)-bi-Koszul algebras. Sci. China Ser. A-Math. 52, 2419–2431 (2009). https://doi.org/10.1007/s11425-009-0194-4

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  • DOI: https://doi.org/10.1007/s11425-009-0194-4

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