Skip to main content
SpringerLink
Log in

Quantum polynomial algebras

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature Cited

  1. J. Alev and M. Chamarie, “Dérivations et automorphismes de quelques algèbres quantiques”,Commun. Algebra,20, No. 6, 1787–1802 (1992).

    MathSciNet  Google Scholar 

  2. J. Alev and F. Dumas, “Sur les corps des fractions de certain algèbres quantiques,”J. Algebra (in press).

  3. V. A. Artamonov, “Projective nonfree modules over group rings of solvable groups”,Mat. Sb.,116, No. 2, 232–244 (1981).

    MATH  MathSciNet  Google Scholar 

  4. V. A. Artamonov, “Projective modules and elementary matrices over rings of skew polynomials”, In:Collective Works on Algebra [in Russian], Moscow State Univ. Press (1989), pp. 6–49.

  5. V. A. Artamonov, “Structure of Hopf algebras”, In:Algebra, Topology, Geometry, Vol. 29,Progress in Science and Technology, Series on, All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1991), pp. 3–63.

    Google Scholar 

  6. V. A. Artamonov, “Projective modules over crossed products,”J. Algebra (in press).

  7. V. A. Artamonov, “Projective modules over quantum polynomials,”Mat. Sb. (in press).

  8. M. Artin, “Geometry of the quantum plane,”Contemp. Math.,124, 1–15 (1992).

    MATH  MathSciNet  Google Scholar 

  9. H. Bass,Algebraic K-Theory, Benjamin, New York (1968).

    Google Scholar 

  10. P. M. Cohn,Free Rings and Their Relations, Academic Press, London, New York (1971).

    Google Scholar 

  11. E. E. Demidov, “On some aspects of quantum group theory,”Usp. Mat. Nauk,48, No. 6, 39–74 (1993).

    MATH  MathSciNet  Google Scholar 

  12. J. Dixmier,Algèbre Enveloppantes, Gauthier-Villards, Paris-Bruxelles-Monréal (1974).

    Google Scholar 

  13. Y. Doi, “Equivalent crossed products for a Hopf algebra,”Commun. Algebra,17, No. 13, 3053–3085 (1989).

    MATH  MathSciNet  Google Scholar 

  14. A. Joseph and G. Letzter, “Separation of variables for quantized enveloping algebras,” Univ. de Paris VI and Wayne State Univ. (1991).

  15. T. Y. Lam, “Serre's conjecture,”Lect. Notes Math.,635 (1978).

  16. M.-P. Malliavin, “L'algèbre d'Heisenberg quantique,”C. R. Acad. Sci., Sér. 1,317, 1099–1102 (1993).

    MATH  MathSciNet  Google Scholar 

  17. Yu. I. Manin,Topics in Noncommutative Geometry, Princeton Univ. Press (1991).

  18. J. C. McConnel and J. J. Pettit, “Crossed products and multiplicative analogues of Weyl algebras,”J. London Math. Soc.,38, No. 1, 47–55 (1988).

    MathSciNet  Google Scholar 

  19. S. Montgomery and L. Small,Noncommutative Rings, Springer-Verlag (1992).

  20. E. E. Makhun, “The Yang-Baxter operators and noncommutative de Rham complexes,”Izv. Rossiisk. Akad. Nauk, Ser. Mat.,58, No. 2, 108–131 (1993).

    Google Scholar 

  21. A. N. Panov, “The division ring of rational functions on GL q (n, K)”,Func. Anal. Appl. (in press).

  22. D. Passman,Infinite Crossed Products, Academic Press, San Diego (1989).

    Google Scholar 

  23. B. Parshal and J.-P. Wang,Quantum Linear Groups, Mem. Amer. Math. Soc., Vol. 89 (1991).

  24. D. Quillen, “Higher algebraicK-theory,”Lect. Notes Math.,341, 85–147 (1973).

    MATH  MathSciNet  Google Scholar 

  25. R. Resco, J. T. Stafford, and L. W. Small, “Krull and global dimensions of semiprime Noetherian PI-rings,”Trans. Am. Math. Soc.,274, 285–295 (1982).

    MathSciNet  Google Scholar 

  26. R. Yu. Reshetikhin, L. A. Tahtadjan, and L. K. Faddeev, “Quantum groups,”Algebra Analiz, No. 1, 193–226 (1990).

    Google Scholar 

  27. J. T. Stafford, “Module structure of Weil algebras,”J. London Math. Soc.,18, No. 2, 429–442 (1978).

    MATH  MathSciNet  Google Scholar 

  28. J. T. Stafford, “On the stable range of right Noetherian rings,”Bull. London Math. Soc.,13, No. 1, 39–41 (1981).

    MATH  MathSciNet  Google Scholar 

  29. J. T. Stafford, “Stably free projective right ideals,”Comp. Math.,54, 63–78 (1985).

    MATH  MathSciNet  Google Scholar 

  30. A. A. Suslin, “AlgebraicK-theory,” In:Algebra, Topology, Geometry, Vol. 20,Progress in Science and Technology, Series on, All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1982), pp. 71–152.

    Google Scholar 

  31. A. A. Suslin, “On the structure of special linear groups over polynomial rings,”Izv. Akad. Nauk SSSR, Ser. Mat.,41, No. 2, 235–252 (1977).

    MATH  MathSciNet  Google Scholar 

  32. M. Sweedler,Hopf Algebras, Benjamin, New York (1969).

    Google Scholar 

  33. H. Yamane, “A P.B.W. theorem for a quantized universal enveloping algebra of typeA n ,”Publ. RIMS Kyoto,25, 503–520 (1989).

    MATH  MathSciNet  Google Scholar 

Download references

Authors
  1. V. A. Artamonov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 26, Algebra-4, 1995.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Artamonov, V.A. Quantum polynomial algebras. J Math Sci 87, 3441–3462 (1997). https://doi.org/10.1007/BF02355445

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02355445

Keywords

Search

Navigation