REFERENCES
- Bavula , V. V. ( 1991 ). Finite-dimensionality of Ext n and Tor n of simple modules over a class of algebras. (Russian) Funktsional. Anal. i Prilozhen. 25 : 80 – 82 .
- Bavula , V. V. ( 1993 ). Generalized Weyl algebras and their representations . St. Petersb. Math. J. 4 : 71 – 93 .
- Bavula , V. V. , Bekkert , V. ( 2000 ). Indecomposable representations of generalized Weyl algebras . Comm. Algebra 28 : 5067 – 5100 .
- Bavula , V. V. , Jordan , D. A. ( 2000 ). Isomorphism problems and groups of automorphisms for generalized Weyl algebras . Trans. Amer. Math. Soc. 353 : 769 – 794 .
- Bavula , V. V. , van Oystaeyen , F. ( 2004 ). Simple modules of the Witten-Woronowicz algebra . J. Algebra 271 : 827 – 845 .
- Bekkert , V. , Benkart , G. , Futorny , V. ( 2004 ). Weight modules for Weyl algebras. In: Kac–Moody Lie Algebras and Related Topics (Proc. Ramanujan Internat. Symp., Chennai, India, 2002). Contemp. Math. Vol. 343. Providence, RI: Amer. Math. Soc., pp. 17–42 .
- Carvalho , P. A. A. B. , Lopes , S. A. ( 2009 ). Automorphisms of generalized down-up algebras . Comm. Alg. 37 : 1622 – 1646 .
- Drozd , Yu. A. , Guzner , B. L. , Ovsienko , S. A. ( 1996 ). Weight modules over generalized Weyl algebras . J. Algebra 184 : 491 – 504 .
- Futorny , V. , Ovsienko , S. Galois orders. arXiv:math/0610069 [math.RT].
- Hartwig , J. T. ( 2006 ). Locally finite simple weight modules over twisted generalized Weyl algebras . J. Algebra 303 : 42 – 76 .
- Hartwig , J. T. Unitarizable weight modules over generalized Weyl algebras. arXiv:0803.0687 [math.RA].
- Kac , V. ( 1990 ). Infinite Dimensional Lie Algebras. , 3rd ed. Cambridge : Cambridge University Press .
- Klimyk , A. , Schmudgen , K. ( 1997 ). Quantum Groups and Their Representations . New York : Springer .
- Mazorchuk , V. , Ponomarenko , M. , Turowska , L. ( 2003 ). Some associative algebras related to U(𝔤) and twisted generalized Weyl algebras . Math. Scand. 92 : 5 – 30 .
- Mazorchuk , V. , Turowska , L. ( 1999 ). Simple weight modules over twisted generalized Weyl algebras . Comm. Alg. 27 : 2613 – 2625 .
- Mazorchuk , V. , Turowska , L. (2002). *-Representations of twisted generalized Weyl constructions. Algebr. Represent. Theory 5:163–186.
- Pusz , W. , Woronowicz , S. L. ( 1989 ). Twisted second quantization . Reports on Math. Phys. 27 : 231 – 257 .
- Rosenberg , A. L. ( 1995 ). Noncommutative Algebraic Geometry and Representations of Quantized Algebras . Dordrecht : Kluwer .
- Futorny , V. , Hartwig , J. T. ( 2010 ). Twisted Weyl Algebras, Crossed Products, and Representations, arXiv: 1005.0341v1 [math.RA], preprint .
- Communicated by T. Lenagan.