Skip to main content

Supersymmetric Bracket Algebra and Invariant Theory

  • Chapter
Topics in Computational Algebra

Abstract

In this section we review some definitions and results in Ref. 9, pp 1–11. Roughly speaking, the supersymmetric algebra is a generalization of the ordinary algebra of polynomials in a set L of variables. Our variables shall be of two kinds: positively signed and negatively signed L=L +L .

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barnabei, M., Brini, A. & Rota, G.-C., On the exterior calculus of invariant theory, J. of Algebra 96 (1985), 120–160.

    Article  MathSciNet  MATH  Google Scholar 

  2. Brini, A., Palareti, A. & Teolis, A., Gordan-Capelli series in superalgebras, Proc. Natl. Acad. Sci. USA, 85 (1988), 1330–1333.

    Article  MathSciNet  MATH  Google Scholar 

  3. Brini, A. & Teolis, A., Young-Capelli symmetrizers in superalgebras, Proc. Natl. Acad. Sci. USA, 86 (1989), 775–778.

    Article  MathSciNet  MATH  Google Scholar 

  4. Désarménien, J., Kung, J. P. S. & Rota, G.-C., Invariant Theory, Young bitableaux and combinatorics, Adv. in Math. 27 (1978), 63–92.

    Article  MATH  Google Scholar 

  5. Dubilet, P., Rota, G.-C. & Stein, J. A., On the foundations of combinatorial theory IX: Combinatorial method in invariant theory, Stud. Appl. Math 53 (1976), 185–216.

    Google Scholar 

  6. Gelfand, M. & Ponomarev, V. A., Problems of linear algebra and classification of quadruples of subspaces in a finite-dimensional vector space, Colloquia Mathematica Societatis Janos Bolyai, (1970) 163–237.

    Google Scholar 

  7. Grace, J. H. & Young A., The algebra of invariants, Chelsea, New York, 1903.

    MATH  Google Scholar 

  8. Grassmann, H., Gesammelte Werke (6 volls.), Teubner, Leipzig, 1911.

    MATH  Google Scholar 

  9. Grosshans, F., Rota, G.-C. & Stein, J. A., Invariant Theory and Superalgebras, Amer. Math. Soc, Providence, RI 69 (1987).

    Google Scholar 

  10. Huang, R. Q., Rota, G.-C. & Stein, J. A., Supersymmetric algebra, supersymmetric space, and invariant theory, Annali Scuola Normale Superiore (Volume dedicated to L. Radicati), (1989) Pisa.

    Google Scholar 

  11. Koh, S. S. (ed), Invariant Theory, Lecture Notes in Math. No. 1278, Springer-Verlag, New York, 1987.

    MATH  Google Scholar 

  12. Kung, J. P. S. (ed.), Yung tableaux in combinatorics, invariant theory and algebra, Academic Press, New York, 1982.

    Google Scholar 

  13. Kung, J. P. S. & Rota G.-C., The invariant theory of binary forms, Bull. Amer. Math. Soc. 10 (1984), 27–85.

    Google Scholar 

  14. Littlewood, D. E., Invariant theory, tensors and group characters, Phil. Trans. Royal Soc. A, 239 (1944), 305–365.

    Article  MathSciNet  MATH  Google Scholar 

  15. McMillan, T. & White, N. L., The dotted straightening algorithm, to appear in J. of Symb. Comp.

    Google Scholar 

  16. McMillan, T. & White, N. L., Cayley factorization, in Proc. International Symposium on Symbolic and Algebraic Computations, Rome, 1988.

    Google Scholar 

  17. Popov, V., Constructive invariant theory, Astérisque 87–88 303–334.

    Google Scholar 

  18. Rota, G.-C. & Stein, J. A., Standard basis in supersymplectic algebras, Proc. Natl. Acad. Sci. USA, 86 (1989), 2521–2524.

    Article  MathSciNet  MATH  Google Scholar 

  19. Rota, G.-C. & Stein, J. A., Supersymmetric Hilbert space, Proc. Natl. Acad. Sci. USA, 87 (1990), 653–657.

    Article  MathSciNet  MATH  Google Scholar 

  20. Rota, G.-C. & Stein, J. A., Applications of Cayley algebras, Colloquio Internazionale sulle Teorie Comninatoriee, Tomo II, Accad. Naz. Lincei, Rome, (1976) 71–97.

    Google Scholar 

  21. Rota, G.-C. & Stein, J. A., Symbolic method in invariant theory, Proc. Natl. Acad. Sci. USA, 83 (1986), 844–847.

    Article  MathSciNet  MATH  Google Scholar 

  22. Springer, T. A., Invariant Theory, Lecture Notes in Math. No. 585, Springer-Verlag, New York, 1977.

    MATH  Google Scholar 

  23. Sturmfels, B. & White, N. L., Gröbner bases and invariant theory, Adv. in Math. 76 (1989), 245–259.

    Article  MathSciNet  MATH  Google Scholar 

  24. Turnbull, H. W., The projective invariants of four medials, Proc. Edinburgh Math. Soc, 7 (2) (1942), 55–72.

    Article  MathSciNet  MATH  Google Scholar 

  25. Young, A., The collected papers of Alfred Young, University of Toronto-Press, Toronto, 1977.

    Google Scholar 

  26. Wallace, A. H., Invariant matrices and Gorden-Capelli series, Proc. London Math. Soc. 2 (1952), 98–127.

    Article  MathSciNet  MATH  Google Scholar 

  27. Weitzenböck, Komplex-Symbolik, Teubner, Leipzig, 1908.

    MATH  Google Scholar 

  28. Weitzenböck, Invariantentheorie, Noordhoff, Groningen, 1923.

    Google Scholar 

  29. White, N. L., Multilinear Cayley factorization, to appear in J. of Symb. Comp.

    Google Scholar 

  30. Whitely, W., Logic and invariant theory, L Invariant theory of projective properties, Trans. Amer. Math. Soc. 177 (1973), 121–139.

    MathSciNet  Google Scholar 

  31. Weyl, H., The classical groups, Princeton Univ. Press, Princeton NJ, 1946.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Huang, R.Q., Rota, GC., Stein, J.A. (1990). Supersymmetric Bracket Algebra and Invariant Theory. In: Cattaneo, G.M.P., Strickland, E. (eds) Topics in Computational Algebra. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3424-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-3424-8_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5514-7

  • Online ISBN: 978-94-011-3424-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics