The Azumaya locus of certain quantum symplectic spaces

References

• Bavula, V. V. (1992). The simple D[X,Y;σ,a]-modules. Ukrain. Math. J. 44(12):1500–1511.
   Google Scholar
• Bavula, V. V. (1993). Generalized Weyl algebras and their representations. St. Petersburg Math. J. 4(1):71–79.
   Google Scholar
• Bavula, V. V. (1996). Global dimension of generalized Weyl algebras. In: Representation Theory of Algebras (Cocoyoc, 1994). CMS Conference Proceedings, Vol. 18. Providence, RI: Amer. Math. Soc., pp. 81–107.
   Google Scholar
• Bavula, V. V. (1999). The simple modules of Ore extensions with coefficients from a Dedekind ring. Commun. Algebra 27(6):2665–2699. DOI: 10.1080/00927879908826587.
   Web of Science ®Google Scholar
• Bavula, V., van Oystaeyen, F. (1997). The simple modules of certain generalized cross product. J. Algebra 194: 521–566. DOI: 10.1006/jabr.1997.7038.
   Web of Science ®Google Scholar
• Bavula, V., Lu, T.(2016). The prime spectrum and simple modules over the quantum spatial ageing algebra. Algebr. Represent. Theory 19(5):1109–1133. DOI: 10.1007/s10468-016-9613-8.
   Web of Science ®Google Scholar
• Bavula, V., Lu, T. (2017). Torsion simple modules over the quantum spatial ageing algebra. Commun. Algebra 45(10):4166–4189. DOI: 10.1080/00927872.2016.1240177.
   Web of Science ®Google Scholar
• Bavula, V., Lu T. (2017). Prime ideals of the enveloping algebra of the Euclidean algebra and a classification of its simple weight modules. J. Math. Phys. 58(1):011701.
   PubMed Web of Science ®Google Scholar
• Bavula, V., Lu, T. (2018). The prime spectrum of the algebra Kq[X,Y]⋊Uq(sl2) and a classification of simple weight modules. J. Noncommutative Geom. 12(3):889–946.
   Web of Science ®Google Scholar
• Brown, K. A., Goodearl, K. R. (2002). Lectures on Algebraic Quantum Groups. Basel; Boton; Berlin: Birkhauser Verlag.
   Google Scholar
• De Concini, C., Processi, C. (1993). Quantum Groups. Lecture Notes in Mathematics, Vol. 1565. New York/Berlin: Springer-Verlag, pp. 31–140.
   Google Scholar
• Faddeev, L. D., Reshtikhin, N. Y., Takhtadzhyan, L. A. (1990). Quantization of Lie groups and Lie algebras. Leningrad Math. J. 1988:193–225.
   Google Scholar
• Gómez-Torrecillas, T., Kaoutit, L., Benyakoub, L. (2001). Prime ideals of the coordinate ring of quantum symplectic space. Commun. Algebra 29(7):3179—3197. DOI: 10.1081/AGB-5016.
   Web of Science ®Google Scholar
• Haynal, H. (2008). PI degree parity in q-skew polynomial rings. J. Algebra 319:4199–4221. DOI: 10.1016/j.jalgebra.2008.01.036.
   Web of Science ®Google Scholar
• Horton, K. L. (2003). The prime and primitive spectra of multiparameter quantum symplectic and Euclidean spaces. Commun. Algebra 31(10):4713–4743. DOI: 10.1081/AGB-120023129.
   Web of Science ®Google Scholar
• Jordan, D. (1995). Finite-dimensional simple modules over certain iterated skew polynomial rings. J. Pure Appl. Algebra 98(1):45–55. DOI: 10.1016/0022-4049(94)00026-F.
   Web of Science ®Google Scholar
• Leroy, A., Matczuk, J. (2011). On q-skew iterated Ore extensions satisfying a polynomial identity. J. Algebra Appl. 10(4):771–781. DOI: 10.1142/S0219498811004938.
   Web of Science ®Google Scholar
• McConnell, J. C., Robson, J. C. (1987). Noncommutative Noetherian Rings. Pure and Applied Mathematics. Graduate Studies in Mathematics 30. Providence, RI: American Mathematical Society.
   Google Scholar
• Musson, I. M. (2001). Ring-theoretic properties of the coordinate rings of quantum symplectic and Euclidean space. (English summary). In: Ring Theory (Granville, OH, 1992). River Edge, NJ: World Scientific Publishers, pp. 248–258.
   Google Scholar
• Oh, S.-Q. (1998). Primitive ideals of the coordinate ring of quantum symplectic space. J. Algebra 174(2):531–552. DOI: 10.1006/jabr.1995.1138.
   Google Scholar
• Rogers, A. (2019). Representations of quantum nilpotent algebras at roots of unity and their completely prime quotients. Ph.D. Thesis, University of Kent.
   Google Scholar
• Zhang, H. (2000). The representations of the coordinate ring of the quantum symplectic space. J. Pure Appl. Algebra 150:95–106. DOI: 10.1016/S0022-4049(99)00023-7.
   Web of Science ®Google Scholar