Advertisement

Eventually Polynomial Betti Sequences over Truncated Path Algebras

  • Marju PurinEmail author
  • Sean Thompson
Article
  • 8 Downloads

Abstract

We study projective resolutions of finitely generated modules over finite-dimensional algebras. We show that every polynomial with integer coefficients and a positive leading term can be eventually realized by a Betti sequence of a simple module over a radn = 0 algebra.

Keywords

Betti sequences Growth of resolutions 

Mathematics Subject Classification (2010)

16E05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

This work was conducted while the second named author was a student at St. Olaf College. The authors would like to thank the college for supporting this project.

References

  1. 1.
    Alperin, J., Evens, L.: Representations, resolutions, and Quillen’s dimension theorem. J. Pure Appl. Algebra 22, 1–9 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Auslander, M., Reiten, I., Smalø, S.O.: Representation Theory of Artin algebras Cambridge Studies in Advanced Mathematics, vol. 36. Cambridge University Press, Cambridge (1995)CrossRefzbMATHGoogle Scholar
  3. 3.
    Assem, I., Simson, D., Skowroński, A.: Elements of the Representation Theory of Associative Algebras. 1: Techniques of Representation Theory, London Mathematical Society Student Texts, vol. 65. Cambridge University Press, Cambridge (2006)CrossRefzbMATHGoogle Scholar
  4. 4.
    Avramov, L.: Infinite Free Resolutions. Six Lectures on Commutative Algebra. Progr. Math., vol. 166, pp 1–118. Birkhauser, Basel (1998)CrossRefGoogle Scholar
  5. 5.
    Avramov, L., Buchweitz, R.-O.: Support varieties and cohomology over complete intersections. Invent. Math. 142, 285–318 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Avramov, L., Gasharov, V., Peeva, I.: Complete Intersection Dimension. Inst. Hautes Études Sci. Publ. Math. 86, 67–114 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Erdmann, K., Holloway, M., Snashall, N., Solberg, Ø., Taillefer, R.: Support varieties for selfinjective algebras. K-theory 33, 67–87 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Eisenbud, D: Homological algebra on a complete intersection, with an application to group representations. Trans. Amer. Math. Soc. 260(1), 35–64 (1980)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Farnsteiner, R.: Tameness and complexity of finite group schemes. Bull. Lond. Math. Soc. 39(1), 63–70 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Rickard, J.: The representation type of selfinjective algebras. Bull. London Math. Soc. 22(6), 540–546 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Tate, J.: Homology of Noetherian rings and local rings. Illinois J. Math. 1, 14–27 (1957)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics, and Computer ScienceSt. Olaf CollegeNorthfieldUSA
  2. 2.West RichlandUSA

Personalised recommendations