Geodesic
Automorphisms of the skew field of rational quantum functions
Sbornik. Mathematics, Tome 191 (2000) no. 12, pp. 1749-1771 Cet article a éte moissonné depuis la source Math-Net.Ru

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The automorphisms of the skew field of fractions of the algebra of quantum polynomials in at least three variables are described. 
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V. A. Artamonov. Automorphisms of the skew field of rational quantum functions. Sbornik. Mathematics, Tome 191 (2000) no. 12, pp. 1749-1771. http://geodesic.mathdoc.fr/item/SM_2000_191_12_a0/

[1] McConnell J. C., Pettit J. J., “Crossed products and multiplicative analogues of Weyl algebras”, J. London Math. Soc., 38:1 (1988), 47–55 | DOI | MR | Zbl

[2] Demidov E. E., Kvantovye gruppy, Faktorial, M., 1998

[3] Artamonov V. A., “Kvantovaya problema Serra”, UMN, 53:4 (1998), 3–76 | MR | Zbl

[4] Artamonov V. A., “Proektivnye moduli nad algebrami kvantovykh mnogochlenov”, Matem. sb., 185:7 (1994), 3–12 | MR | Zbl

[5] Artamonov V. A., “Quantum polynomial algebras”, J. Math. Sci., 87:3 (1997), 3441–3462 | DOI | MR | Zbl

[6] Brown K. A., Goodearl K. R., “Prime spectra of quantum semisimple groups”, Trans. Amer. Math. Soc., 348:6 (1996), 2465–2501 | DOI | MR

[7] Goodearl K. G., Letzter E. S., “Prime factor of the coordinate ring of quantum matrices”, Proc. Amer. Math. Soc., 121:4 (1994), 1017–1025 | DOI | MR | Zbl

[8] Goodearl K. G., Letzter E. S., “Prime and primitive spectra of multiparameter quantum affine spaces”, Trends in ring theory, Proceedings of a conference (Miskolc, Hungary, July 15–20, 1996), Amer. Math. Soc., Providence, RI, 1998, 39–58 | MR | Zbl

[9] Alev J., Chamarie M., “Dérivations et automorphismes de quelques algèbres quantiques”, Comm. Algebra, 20:6 (1992), 1787–1802 | DOI | MR | Zbl

[10] Kirkman E., Procesi C., Small L., “A $q$-analog for the Virasoro algebra”, Comm. Algebra, 20:10 (1994), 3755–3774 | DOI | MR

[11] Osborn J. M., Passman D. S., “Derivations of skew polynomial rings”, J. Algebra, 176:2 (1995), 417–448 | DOI | MR | Zbl

[12] Alev J., Dumas F., “Automorphismes de certains complétés de corps de Weyl quantiques”, Collect. Math., 46:1–2 (1995), 1–9 | MR | Zbl

[13] Alev J., Dumas F., “Invariants du corps de Weyl sous l'action de groupes finis”, Comm. Algebra, 25:5 (1997), 1655–1672 | DOI | MR | Zbl

[14] Artamonov V. A., Cohn P. M., “On the skew field of rational functions on the quantum plane”, J. Math. Sci., 93:6 (1999), 824–829 | DOI | MR | Zbl

[15] Iskovskikh V. A., “Obrazuyuschie i sootnosheniya v dvumernoi gruppe Kremony”, Vestn. MGU. Ser. 1. Matem., mekh., 1983, no. 5, 43–48 | MR | Zbl

[16] Maltsev A. I., “O vklyuchenii gruppovykh algebr v algebry s deleniem”, Dokl. AN SSSR, 60 (1948), 1499–1501 | MR | Zbl

[17] Liu Zhongkui, “$PF$-rings of generalized power series”, Bull. Austral. Math. Soc., 57 (1998), 427–432 | DOI | MR | Zbl

[18] Ribenboim P., “Rings of generalized power series. II: units and zero divisors”, J. Algebra, 168 (1994), 71–89 | DOI | MR | Zbl

[19] Ribenboim P., “Semisimple rings and von Neumann regular rings of generalized power series”, J. Algebra, 198 (1997), 327–338 | DOI | MR | Zbl