Geodesic
GK DIMENSION AND LOCALLY NILPOTENT SKEW DERIVATIONS
Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 555-567

Voir la notice de l'article provenant de la source Cambridge University Press

Let A be a domain over an algebraically closed field with Gelfand–Kirillov dimension in the interval [2,3). We prove that if A has two locally nilpotent skew derivations satisfying some natural conditions, then A must be one of five algebras. All five algebras are Noetherian, finitely generated, and have Gelfand–Kirillov dimension equal to 2. We also obtain some results comparing the Gelfand–Kirillov dimension of an algebra to its subring of invariants under a locally nilpotent skew derivation. 
BERGEN, JEFFREY; GRZESZCZUK, PIOTR. GK DIMENSION AND LOCALLY NILPOTENT SKEW DERIVATIONS. Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 555-567. doi: 10.1017/S0017089514000482
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[1] 1.Bavula, V. V., Generators and defining relations for rings of invariants of commuting locally nilpotent derivations or automorphims, J. London Math. Soc. 76 (1) (2007), 148–164. Google Scholar | DOI

[2] 2.Bell, J. P. and Smoktunowicz, A., Rings of differential operators on curves, Isr. J. Math. 192 (1) (2012), 297–310. Google Scholar | DOI

[3] 3.Bergen, J. and Grzeszczuk, P., On rings with locally nilpotent skew derivations, Commun. Algebra, 39 (2011), 3698–3708. Google Scholar | DOI

[4] 4.Borho, W. and Kraft, H., Über die Gelfand–Kirillov dimension Math. Ann. 220 (1976), 1–24. Google Scholar | DOI

[5] 5.Chung, L. O. and Luh, J., Nilpotency of derivations on an ideal, Proc. Am. Math. Soc. 90 (2) (1984), 211–214. Google Scholar | DOI

[6] 6.Huh, C. and Kim, C. O., Gelfand–Kirillov dimension of skew polynomial rings of automorphism type, Commun. Algebra 24 (7) (1996), 2317–2323. Google Scholar | DOI

[7] 7.Krempa, J., Radicals and derivations of algebras, Proceedings of Eger Conference (North Holland, 1982). Google Scholar

[8] 8.Krause, G. R. and Lenagan, T. H., Growth of algebras and Gelfand–Kirillov dimension, Graduate Studies in Mathematics, vol. 22, (Amer. Math. Soc., Providence, 2000). Google Scholar

[9] 9.Mcconnell, J. C. and Robson, J. C., Noncommutative Noetherian rings, Pure and Applied Mathematics (John Wiley & Sons, Chichester, 1987). Google Scholar

[10] 10.Small, L. W. and Warfield, R. B. Jr., Prime affine algebras of Gelfand–Kirillov dimension one, J. Algebra 91 (2) (1984), 386–389. Google Scholar | DOI

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