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On Quantized Algebra of Wess–Zumino Differential Operators at Roots of Unity

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Abstract

A quantum deformation of the algebra of differential operators is studied.

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References

  1. Chari, V. and Pressley, A.: A Guide to Quantum Groups, Cambridge University Press, Cambridge, 1994.

    Google Scholar 

  2. Demidov, E. E.: Some aspects of the theory of quantum groups, Uspekhi Mat. Nauk 48(6) (1993), 39–74 (Russian); English transl. in Russian Math. Surveys 48(6) (1993), 41–79.

    Google Scholar 

  3. Jimbo, M.: A q-analog of U(\(g\) l(N + 1)), Hecke algebra and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), 247–252.

    Google Scholar 

  4. Kassel, C.: Quantum Groups, Springer-Verlag, New York, 1995.

    Google Scholar 

  5. Manin, Yu. I.: Quantum groups and non-commutative geometry, Lecture notes, CRM, Université de Montréal, 1989.

  6. Reshetikhin, N. Yu., Takhtajan, L. A., and Faddeev, L. D.: Quantization of Lie groups and Lie algebras, Algebra i Analiz 1 (1990), 178–206 (Russian); English transl. in Leningrad Math. J. 1 (1990), 193–225.

    Google Scholar 

  7. Verbovetsky, A. M.: Lagrangian formalism over graded algebras, J. Geom. Phys. 18 (1996), 195–214; hep-th/9407037.

    Google Scholar 

  8. Verbovetsky, A. M.: Differential operators on quantum spaces, Acta Appl. Math. 49 (1997), 339–361 (this issue).

    Google Scholar 

  9. Vinogradov, A. M.: The logic algebra for the theory of linear differential operators, Dokl. Akad. Nauk SSSR 205 (1972), 1025–1028 (Russian); English transl. in Soviet Math. Dokl. 13 (1972), 1058–1062.

    Google Scholar 

  10. Vinogradov, A. M.: On the algebro-geometric foundations of Lagrangian field theory, Dokl. Akad. Nauk SSSR 236 (1977), 284–287 (Russian); English transl. in Soviet Math. Dokl. 18 (1977), 1200–1204.

    Google Scholar 

  11. Vinogradov, A. M.: The C-spectral sequence, Lagrangian formalism, and conservation laws, J. Math. Anal. Appl. 100 (1984), 1–129; I. The linear theory.

    Google Scholar 

  12. Vinogradov, A. M., Krasil'shchik, I. S., and Lychagin, V. V.: Introduction to the Geometry of Nonlinear Differential Equations, Nauka, Moscow, 1986 (Russian); English transl. Geometry of Jet Spaces and Nonlinear Partial Differential Equations, Gordon and Breach, New York, 1986.

    Google Scholar 

  13. Wess, J. and Zumino, B.: Covariant differential calculus on the quantum hyperplane, Nuclear Phys. B Proc. Suppl. 18 (1990), 302–312.

    Google Scholar 

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Verbovetsky, A. On Quantized Algebra of Wess–Zumino Differential Operators at Roots of Unity. Acta Applicandae Mathematicae 49, 363–370 (1997). https://doi.org/10.1023/A:1005898524274

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