Skip to main content
SpringerLink
Log in

Gröbner–Shirshov basis and the minimal projective resolution of U +q (G 2)

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper, by using the Anick’s resolution and Gröbner–Shirshov basis for quantized enveloping algebra of type G 2, we compute the minimal projective resolution of the trivial module of U +q (G 2) and as an application we compute the global dimension of U +q (G 2).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anick, D. J.: On the homology of associative algebras. Trans. Amer. Math. Soc., 296(2), 641–659 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. Avramov, L. L., Foxby, H.-B., Halperin, S.: Differencial Graded Homological Algebra, inpreparation, 2007

    Google Scholar 

  3. Bokut, L. A., Malcolmson, P.: Gröbner–Shirshov basis for quantum enveloping algebras. Israel J. Math., 96, 97–113 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. Lorentz, M. E., Lorentz, M.: On crossed products of Hopf algebras. Proc. Amer. Math. Soc., 123, 33–38 (1995)

    Article  MathSciNet  Google Scholar 

  5. Ren, Y. H., Obul, A.: Gröbner–Shirshov basis of quantum group of type G2. Comm. Algebra, 39(5), 1510–1518 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ringel, C. M.: Hall algebras and quantum groups. Invent. Math., 101, 583–592 (1990)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, China

    Ling Ling Mao & Abdukadir Obul

Authors
  1. Ling Ling Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdukadir Obul
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdukadir Obul.

Additional information

Supported by National Natural Science Fuondation of China (Grant No. 11361056)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mao, L.L., Obul, A. Gröbner–Shirshov basis and the minimal projective resolution of U +q (G 2). Acta. Math. Sin.-English Ser. 32, 213–226 (2016). https://doi.org/10.1007/s10114-016-5099-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-016-5099-x

Keywords

MR(2010) Subject Classification

Search

Navigation