Skip to main content

Matrix factorizations of homogeneous polynomials

Part of the Lecture Notes in Mathematics book series (LNM,volume 1352)

Keywords

  • Matrix Factorization
  • Homogeneous Polynomial
  • Clifford Algebra
  • Diagonal Form
  • Hilbert Series

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. F. Atiyah, R. Bott, A. Shapiro, Clifford modules, Topology 3, Suppl. (1964), 3–38.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. J. Backelin, La séire de Poincaré-Betti d'une algèbre graduée de type fini à une relation est rationnelle, C. R. Acad. Sc. Paris 287 (1978), 846–849.

    MathSciNet  MATH  Google Scholar 

  3. G. M. Bergman, The diamond lemma for ring theory, Advances in Math. 29 (1978), 178–218.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. R. O. Buchweitz, D. Eisenbud, J. Herzog, Cohen-Macaulay modules on quadrics, to appear in the Proceedings of the Lambrecht Conference ‘Representations of algebras, singularities and vector bundels’ (S.L.N.).

    Google Scholar 

  5. J. P. Brennan, J. Herzog, B. Ulrich, Maximally generated Cohen-Macaulay modules, to appear in Math. Scand..

    Google Scholar 

  6. L. N. Childs, Linearizing of n-ic forms and generalized Clifford algebras, Linear and Multilinear Algebra 5 (1978), 267–278.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. D. Eisenbud, Homological algebra on a complete intersection with an application to group representations, Trans. AMS 260 (1980), 35–64.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. N. Heerema, An algebra determined by a binary qubic form, Duke math J. 21 (1954), 423–444.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. J. Herzog, M. Kühl, Maximal Cohen-Macaulay modules over Gorenstein rings and Bourbaki-sequences, Advanced Studies in Pure Mathematics 11, 1987, Commutative Algebra and Combinatorics.

    Google Scholar 

  10. J. Herzog, H. Sanders, The Grothendieck group of invariant rings and of simple hypersurface singularities, to appear in the Proceedings of the Lambrecht Conference ‘Representations of algebras, singularities and vector bundels’ (S.L.N.).

    Google Scholar 

  11. H. Knörrer, Maximal Cohen-Macaulay modules on hypersurface singularities I, Invent. Math. 88 (1985), 153–164.

    CrossRef  MATH  Google Scholar 

  12. F. W. Long, Generalized Clifford algebras and dimodule algebras, J. London Math. Soc. (2) 13 (1976), 438–442.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. J. Milnor, Introduction to algebraic K-theory, (Annals of Math. Studies No. 72, Princeton, 1971).

    Google Scholar 

  14. N. Roby, Algèbres de Clifford des formes polynomes, C. R. Acad. Sc. Paris 268 (1969), 484–486.

    MathSciNet  MATH  Google Scholar 

  15. W. Scharlau, Quadratic and Hermitian Forms, Grundlehren 270, Springer-Verlag, Berlin Heidelberg, 1985.

    CrossRef  Google Scholar 

  16. U. Storch, Die Picard-Zahlen der Singularitäten G2S n , J. Reine Angew. Math. 350 (1984), 188–202.

    MathSciNet  MATH  Google Scholar 

  17. B. Ulrich, Gorenstein rings and modules with high numbers of generators, Math. Z. 188 (1984), 23–32.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Backelin, J., Herzog, J., Sanders, H. (1988). Matrix factorizations of homogeneous polynomials. In: Avramov, L.L., Tchakerian, K.B. (eds) Algebra Some Current Trends. Lecture Notes in Mathematics, vol 1352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082014

Download citation

  • DOI: https://doi.org/10.1007/BFb0082014

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50371-2

  • Online ISBN: 978-3-540-45994-1

  • eBook Packages: Springer Book Archive