Classification of the simple modules of the quantum Weyl algebra and the quantum plane
Bavula, Vladimir
Banach Center Publications, Tome 38 (1997), p. 193-201 / Harvested from The Polish Digital Mathematics Library
Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:252250
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     author = {Bavula, Vladimir},
     title = {Classification of the simple modules of the quantum Weyl algebra and the quantum plane},
     journal = {Banach Center Publications},
     volume = {38},
     year = {1997},
     pages = {193-201},
     zbl = {0890.17012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p193bwm}
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Bavula, Vladimir. Classification of the simple modules of the quantum Weyl algebra and the quantum plane. Banach Center Publications, Tome 38 (1997) pp. 193-201. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv40z1p193bwm/

[000] [AP 1] D. Arnal and G. Pinczon, On algebraically irreducible representations of the Lie algebra sl(2), J. Math. Phys. 15 (1974), 350-359. | Zbl 0298.17003

[001] [AP 2] D. Arnal and G. Pinczon, Idéaux à gauche dans les quotients simples de l'algèbre enveloppante de sl(2), Bull. Soc. Math. France 101 (1973), 381-395. | Zbl 0357.17008

[002] [Bam] K. S. Bamba, Sur les idéaux maximaux de l’algèbre de Weyl A1, C. R. Acad. Sci. Paris (A) 283 (1976), 71-74.

[003] [BVO] V. V. Bavula, and F. van Oystaeyen, The simple modules of certain generalized crossed products, Trans. Amer. Math. Soc. (to appear). | Zbl 0927.16002

[004] [Bav 1] V. V. Bavula, The finite-dimensionality of Extn’s and Torn’s of simple modules over a class of algebras, Funktsional. Anal. i Prilozhen. 25 (1991),no. 3, 80-82.

[005] [Bav 2] V. V. Bavula, The simple D[X,Y;σ,a]-modules, Ukrainian Math. J. 44 (1992), 1628-1644. | Zbl 0810.16003

[006] [Bav 3] V. V. Bavula, Generalized Weyl algebras, kernel and tensor-simple algebras, their simple modules, Representations of algebras. Sixth International Conference, August 19-22, 1992. CMS Conference proceedings (V. Dlab and H. Lenzing Eds.), v. 14 (1993), 83-106. | Zbl 0806.17023

[007] [Bav 4] V. V. Bavula, Generalized Weyl algebras and their representations, Algebra i Analiz, 4 (1992), no. 1, 75-97; English trans. in St.Petersburg Math. J. 4 (1993), no. 1, 71-92.

[008] [Bav 5] V. V. Bavula, Tensor homological minimal algebras, global dimension of the tensor product of algebras and of generalized Weyl algebras, Bull. Sci. Math. 120 (1996), 293-335. | Zbl 0855.16010

[009] [Bav 6] V. V. Bavula, Global dimension of generalized Weyl algebras. Proceedings of the 7th Int. Conf. on Represent. of Algebras, August 22-26, 1994. CMS Conference proceedings (R. Bautista, R. Martinez-Villa and J. A. de la Pena Eds), 18 (1996), 81-107. | Zbl 0857.16025

[010] [Bl 1] R. E. Block, Classification of the irréducible representations of sl(2, C), Bull. Amer. Math. Soc., 1 (1979), 247-250. sl(2) and of the Weyl algebra, Adv. Math. 39 (1981), 69-110.

[011] [Bl 2] R. E. Block, The irreducible representations of the Weyl algebra A1, in ’Séminaire d’Algèbre Paul Dubreil (Proceedings, Paris 1977-1978)’ (M. P. Malliavin, Ed.), Lecture Notes in Mathematics no. 740, pp. 69-79, Springer-Verlag, Berlin/New York, 1979.

[012] [Bl 3] R. E. Block, The irreducible representations of the Lie algebra sl(2) and of the Weyl algebra, Adv. Math. 39 (1981), 69-110. | Zbl 0454.17005

[013] [Di 1] J. Dixmier, Représentations irréductibles des algèbres de Lie nilpotentes, An. Acad. Brasil. Ci. 35 (1963), 491-519.

[014] [Di 2] J. Dixmier, Sur les algèbres de Weyl, Bull. Soc. Math. France 96 (1968), 209-242.

[015] [EL] A. Van den Essen and A. Levelt, An explicit description of all simple K[[X]][∂]-modules, Contemp. Math., 130 (1992), 121-131. | Zbl 0812.16037

[016] [Jac] N. Jacobson, The Theory of Rings, Amer. Math. Soc., Providence, R. I., 1943.

[017] [Jor 1] D. A. Jordan, Krull and global dimension of certain iterated skew polynomial rings, Contemp. Math., 130 (1992), 201-213. | Zbl 0779.16011

[018] [Jor 2] D. A. Jordan, Primitivity in skew Laurent polynomial rings and related rings, Math. Z., 213 (1993), 353-371. | Zbl 0797.16037

[019] [Hod 1] T. J. Hodges, Noncommutative deformation of type-A Kleinian singularities, J. Algebra 161 (1993), no. 2, 271-290. | Zbl 0807.16029

[020] [Le] F. W. Lemire, Existence of weight space decompositions for irreducible representations of simple Lie algebras, Canad. Math. Bull. 14 (1971), 113-115. | Zbl 0215.09502

[021] [Ma] M.-P. Malliavin, L'algèbre d'Heisenberg quantique, C. R. Acad. Sci. Paris, Sér. 1, 317 (1993), 1099-1102.

[022] [MR] J. C. McConnell and J. C. Robson, Homomorphism and extensions of modules over certain polynomial rings, J. Algebra 26 (1973), 319-342. | Zbl 0266.16031

[023] [Sm] S. P. Smith, A class of algebras similar to the enveloping algebra of sl(2), Trans. Amer. Math. Soc. 322 (1990), 285-314.

[024] [Sm 1] S. P. Smith, Quantum qroups: An introduction and survey for ring theoretists, in Noncommutative Rings (S.Montgomery and L.W.Small, Eds.) pp. 131-178, MSRI publ. 24, Springer-Verlag, Berlin (1992).

[025] [Za] C. Zachos, Elementary paradigms of quantum algebras, Contemporary Math. 134 (1992), 351-377. | Zbl 0784.17028