REFERENCES
- Amitsur , S. A. ( 1958 ). Commutative linear differential operators . Pacific J. Math. 8 : 1 – 10 . [CSA]
- Artamonov , V. A. , Cohn , P. M. ( 1999 ). The skew field of rational functions on the quantum plane . Algebra, 11. J. Math. Sci. (New York) 93 ( 6 ): 824 – 829 . [CSA]
- Bass , H. , Meisters , G. ( 1985 ). Polynomial flows in the plane . Adv. in Math. 55 ( 2 ): 173 – 208 . [CSA] [CROSSREF]
- Bass , H. , Connel E. H. , Wright , D. ( 1982 ). The Jacobian Conjecture: reduction of degree and formal expansion of the inverse . Bull. Amer. Math. Soc. (New Series) 7 : 287 – 330 . [CSA]
- Bavula , V. V. ( 1992 ). Generalized Weyl algebras and their representations . Algebra i Analiz 4 ( 1 ): 75 – 97 ; translation in St. Petersburg Math. J. ( 1993 ). 4 ( 1 ): 71 – 92 . [CSA]
- Bavula , V. V. ( 2001 ). A Question of Rentschler and the problem of Dixmier . Ann. of Math. 154 ( 3 ): 683 – 702 . [CSA]
- Bavula , V. V. ( 2005a ). Dixmier's Problem 5 for the Weyl algebra . J. Algebra 283 ( 2 ): 604 – 621 . [CSA] [CROSSREF]
- Bavula , V. V. ( 2005b ). Dixmier's Problem 6 for somewhat commutative algebras and Dixmier's Problem 3 for the ring of differential operators on a smooth irreducible affine curve . J. Algebra and Its Appl. 4 ( 5 ): 577 – 586 . [CSA] [CROSSREF]
- Bavula , V. V. ( 2005c ). Dixmier's Problem 6 for the Weyl algebra (the generic type problem) . ArXiv:math.RA/0402244 . [CSA]
- Borho , W. , Gabriel , P. Rentschler , R. ( 1973 ). Primideale in Einhüllenden Auflösbarer Lie-Algebren (Beschreibung durch Bahnenräume). (German) . Lecture Notes in Mathematics . Vol. 357 . Berlin-New York : Springer-Verlag .
- Crawley-Boevey , W. , Holland , M. ( 1998 ). Noncommutative deformations of Kleinian singularities . Duke Math. J. 92 ( 3 ): 605 – 635 . [CSA] [CROSSREF]
- Dixmier , J. ( 1966 ). Repr´esentation irr´educibles des algébres de Lie resolubles . J. Math. Pures et Appl. 45 : 1 – 66 . [CSA]
- Dixmier , J. ( 1968 ). Sur les algèbres de Weyl . Bull. Soc. Math. France 96 : 209 – 242 . [CSA]
- Hodges , T. ( 1993 ). Noncommutative deformations of type-A Kleinian singularities . J. Algebra 161 ( 2 ): 271 – 290 . [CSA] [CROSSREF]
- Goodearl , K. R. ( 1983 ). Centralizers in differential, pseudodifferential, and fractional differential operator rings . Rocky Mountain J. Math. 13 ( 4 ): 573 – 618 . [CSA]
- Joseph , A. ( 1975 ). The Weyl algebra—semisimple and nilpotent elements . Amer. J. Math. 97 ( 3 ): 597 – 615 . [CSA]
- Krause , G. , Lenagan , T. ( 2000 ). Growth of algebras and Gelfand–Kirillov dimension . Revised edition . Graduate Studies in Mathematics, 22 . Providence , RI : Amer. Math. Soc.
- Kirkman , E. E. , Small , L. W. ( 1992 ). q-analogs of harmonic oscillators and related rings . Wake Forest University and University of California .
- Malliavin , M.-P. ( 1993 ). L'algèbre d'Heisenberg quantique . C. R. Acad. Sci. Paris 317 ( 1 ): 1099 – 1102 . [CSA]
- Mazorchuk , V. (2001). A note on centralizers in q-deformed Heisenberg algebras. AMA Algebra Montp. Announc. Paper 2, pp. 6. [CSA]
- McConnell , J. C. , Robson , J. C. ( 1973 ). Homomorphisms and extensions of modules over certain differential polynomial rings . J. Algebra 26 : 319 – 342 . [CSA] [CROSSREF]
- McConnell , J. C. , Robson , J. C. ( 2001 ). Noncommutative Noetherian Rings . With the cooperation of L. W. Small. Revised edition . Graduate Studies in Mathematics, 30 . Providence , RI : American Mathematical Society .
- Communicated by T. Lenagan.