Grassmann geometric calculus, invariant theory and superalgebras

  • A. Brini
  • F. Regonati
  • A. G. B. Teolis


The idea of exploring and developing the deep connections between the theory of Cayley-Grassmann algebras and the invariant theory of skew-symmetric tensors was a recurrent theme of Rota’s mathematical work.


Invariant Theory Polarization Operator Leibniz Rule Divided Power Free Monoid 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Abe, E. (1977): Hopf algebras. Cambridge University Press, CambridgeGoogle Scholar
  2. [2]
    Barnabei, M., Brini, A. (1988): The Littlewood-Richardson rule for co-Schur modules. Adv. Math. 67, 143–173MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Barnabei, M., Brini, A., Rota, G.-C. (1985): On the exterior calculus of invariant theory. J. Algebra 96, 120–160MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Bravi, P., Brini, A. (2000): Remarks on invariant geometric calculus. Cayley-Grassmann algebras and geometric Clifford algebrasGoogle Scholar
  5. [5]
    Brini, A., Huang, R.Q., Teolis, A. (1992): The umbral symbolic method for supersymmetric tensors. Adv. Math. 96, 123–193MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Brini, A., Palareti, A., Teolis, A. (1988): Gordan-Capelli series in superalgebras. Proc. Nat. Acad. Sci. U.S.A. 85, 1330–1333MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    Brini, A., Regonati, F., Teolis, A. (1999): Multilinear algebra over supersymmetric rings. Adv. Math. 145, 98–158MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    Brini, A., Teolis, A. (1989): Young-Capelli symmetrizers in superalgebras. Proc. Nat. Acad. Sci. U.S.A. 86, 775–778MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    Brini, A., Teolis, A. (1995): Capelli’s method of variabili ausiliarie, superalgebras and geometric calculus. In: White, N.L. (ed.) Invariant Methods in Discrete and Computational Geometry. Kluwer, Dordrecht, pp. 59–75Google Scholar
  10. [10]
    Brini, A., Teolis, A. (1996): Grassmann progressive and regressive products and CG-Algebras. In: Schubring, G. (ed.) Hermann Günther Graßmann (1809–1877): Visionary Mathematician, Scientist and Neohumanist Scholar. Kluwer, Dordrecht, pp. 231–242Google Scholar
  11. [11]
    Capelli, A. (1902): Lezioni sulla teoria delle forme algebriche: Pellerano, NapoliGoogle Scholar
  12. [12]
    Chambadal, L., Ovaert, J.L. (1968): Algèbre linéaire et algèbre tensorielle. Dunod, ParisGoogle Scholar
  13. [13]
    Chan, W. (1998): Classification of trivectors in 6-D space. In: Sagan, B.E. and Stanley, R.P. (eds.) Mathematical Essays in Honor of G.-C. Rota. Birkhäuser Boston, Boston, MA, pp. 63–110CrossRefGoogle Scholar
  14. [14]
    Chan, W., Rota, G.-C., Stein, J. (1995): The power of positive thinking. In: White, N.L. (ed.) Invariant Methods in Discrete and Computational Geometry. Kluwer, Dordrecht, pp.1–36Google Scholar
  15. [15]
    De Concini, C., Procesi, C. (1976): A characteristic-free approach to invariant theory. Adv. Math. 21, 330–354MATHCrossRefGoogle Scholar
  16. [16]
    Doubilet, P., Rota, G.-C., Stein, J. (1974): On the foundations of combinatorial theory: IX. Combinatorial methods in invariant theory. Studies in Appl. Math. 53, 185–216MathSciNetMATHGoogle Scholar
  17. [17]
    Grassmann, H.G. (1894–1911): Hermann Graßmanns gesammelte mathematische und physikalische Werke. (3 vols.) Engel, F. (ed.) Teubner, LeipzigGoogle Scholar
  18. [18]
    Grosshans, F.D., Rota, G.-C., Stein, J.A. (1987): Invariant theory and superalgebras. (CBMS Regional Conference Series in Mathematics, vol. 69, American Mathematical Society, Providence, RIGoogle Scholar
  19. [19]
    Gurevich, G.B. (1964): Foundations of the theory of algebraic invariants. Noordhoff, GroningenGoogle Scholar
  20. [20]
    Peano, G. (1888): Calcolo geometrico secondo 1’Ausdehnungslehre di H.G. Grassmann preceduto dalle operazioni della logica deduttiva. Fratelli Bocca, Torino. Translation: (2000): Geometric calculus. Kannenberg, L.C. (translator). Birkhäuser Boston, Boston, MAGoogle Scholar
  21. [21]
    Schubring, G. (ed.) (1996): Hermann Günther Graßmann (1809–1877): visionary mathematician, scientist and neohumanist scholar. Kluwer, DordrechtGoogle Scholar
  22. [22]
    Stewart, I. (1986): Herrmann Grassmann was right. Nature 321, 17MathSciNetMATHCrossRefGoogle Scholar
  23. [23]
    Weitzenböck, R. (1923): Invariantentheorie. Noordhoff, GroningenGoogle Scholar
  24. [24]
    Weyl, H. (1946): The classical groups. Their invariants and representation, 2nd edition. Princeton University Press, Princeton, NJGoogle Scholar
  25. [25]
    White, N.L. (ed.) (1995): Invariant methods in discrete and computational geometry. Kluwer, DordrechtGoogle Scholar

Copyright information

© Springer-Verlag Italia 2001

Authors and Affiliations

  • A. Brini
  • F. Regonati
  • A. G. B. Teolis

There are no affiliations available

Personalised recommendations