Abstract
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.
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References
Abe, E. (1977): Hopf algebras. Cambridge University Press, Cambridge
Barnabei, M., Brini, A. (1988): The Littlewood-Richardson rule for co-Schur modules. Adv. Math. 67, 143–173
Barnabei, M., Brini, A., Rota, G.-C. (1985): On the exterior calculus of invariant theory. J. Algebra 96, 120–160
Bravi, P., Brini, A. (2000): Remarks on invariant geometric calculus. Cayley-Grassmann algebras and geometric Clifford algebras
Brini, A., Huang, R.Q., Teolis, A. (1992): The umbral symbolic method for supersymmetric tensors. Adv. Math. 96, 123–193
Brini, A., Palareti, A., Teolis, A. (1988): Gordan-Capelli series in superalgebras. Proc. Nat. Acad. Sci. U.S.A. 85, 1330–1333
Brini, A., Regonati, F., Teolis, A. (1999): Multilinear algebra over supersymmetric rings. Adv. Math. 145, 98–158
Brini, A., Teolis, A. (1989): Young-Capelli symmetrizers in superalgebras. Proc. Nat. Acad. Sci. U.S.A. 86, 775–778
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. 59–75
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. 231–242
Capelli, A. (1902): Lezioni sulla teoria delle forme algebriche: Pellerano, Napoli
Chambadal, L., Ovaert, J.L. (1968): Algèbre linéaire et algèbre tensorielle. Dunod, Paris
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. 63–110
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.1–36
De Concini, C., Procesi, C. (1976): A characteristic-free approach to invariant theory. Adv. Math. 21, 330–354
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, 185–216
Grassmann, H.G. (1894–1911): Hermann Graßmanns gesammelte mathematische und physikalische Werke. (3 vols.) Engel, F. (ed.) Teubner, Leipzig
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, RI
Gurevich, G.B. (1964): Foundations of the theory of algebraic invariants. Noordhoff, Groningen
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, MA
Schubring, G. (ed.) (1996): Hermann Günther Graßmann (1809–1877): visionary mathematician, scientist and neohumanist scholar. Kluwer, Dordrecht
Stewart, I. (1986): Herrmann Grassmann was right. Nature 321, 17
Weitzenböck, R. (1923): Invariantentheorie. Noordhoff, Groningen
Weyl, H. (1946): The classical groups. Their invariants and representation, 2nd edition. Princeton University Press, Princeton, NJ
White, N.L. (ed.) (1995): Invariant methods in discrete and computational geometry. Kluwer, Dordrecht
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Brini, A., Regonati, F., Teolis, A.G.B. (2001). Grassmann geometric calculus, invariant theory and superalgebras. In: Crapo, H., Senato, D. (eds) Algebraic Combinatorics and Computer Science. Springer, Milano. https://doi.org/10.1007/978-88-470-2107-5_9
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DOI: https://doi.org/10.1007/978-88-470-2107-5_9
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