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Articles

Tauvel’s height formula for quantum nilpotent algebras

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Pages 4194-4209 | Received 16 May 2018, Accepted 19 Jan 2019, Published online: 13 Apr 2019

References

  • Bell, A. D., Sigurdsson, G. (1989). Catenarity and Gelfand–Kirillov dimension in Ore extensions. J. Algebra 127(2):409–425. DOI:10.1016/0021-8693(89)90261-5.
  • Bell, J. A., Launois, S. (2010). On the dimension of H-strata in quantum algebras. Algebra Number Theory 4(2):175–200. DOI:10.2140/ant.2010.4.175.
  • Bell, J. A., Launois, S., Nguyen, N. (2009). Dimension and enumeration of primitive ideals in quantum algebras. J. Algebr. Comb. 29(3):269–294. DOI:10.1007/s10801-008-0132-5.
  • Brown, K. A., and Goodearl, K. R. (2002). Lectures on algebraic quantum groups. Advanced courses in mathematics CRM Barcelona, Birkhäuser, Basel.
  • Cauchon, G. (2003). Effacement des dérivations et spectres premiers des algèbres quantiques. J. Algebra 260(2):476–518. DOI:10.1016/S0021-8693(02)00542-2.
  • Cauchon, G. (2003). Spectre premier de Oq(Mn(k)). image canonique et séparation normale. J. Algebra 260:519–569. DOI:10.1016/S0021-8693(02)00543-4.
  • Goodearl, K. R., Launois, S., Lenagan, T. H. (2011). Totally nonnegative cells and matrix Poisson varieties. Adv. Math 226(1):779–826. DOI:10.1016/j.aim.2010.07.010.
  • Goodearl, K. R., Launois, S., Lenagan, T. H. (2011). Torus-invariant prime ideals in quantum matrices, totally nonnegative cells and symplectic leaves. Math. Z 269(1–2):29–45. DOI:10.1007/s00209-010-0714-5.
  • Goodearl, K. R., Lenagan, T. H. (1996). Catenarity in quantum algebras. J. Pure Appl. Algebra 111(1–3):123–142. DOI:10.1016/0022-4049(95)00120-4.
  • Goodearl, K. R., Letzter, E. S. (1994). Prime ideals in skew and q-skew polynomial rings. Memoirs of the AMS 109(521):0. DOI:10.1090/memo/0521.
  • Goodearl, K. R., Letzter, E. S. (1994). Prime factor algebras of the coordinate ring of quantum matrices. Proc. Amer. Math. Soc. 121(4):1017–1025. DOI:10.1090/S0002-9939-1994-1211579-1.
  • Goodearl, K. R., Letzter, E. S. (2000). The Dixmier-Moeglin equivalence in quantum matrices and quantum Weyl algebras. Trans. Amer. Math. Soc. 352(03):1381–1403. DOI:10.1090/S0002-9947-99-02345-4.
  • Goodearl, K. R., Warfield, R. B., Jr. (2004). An Introduction to Noncommutative Noetherian Rings. 2nd ed. London Math. Soc. Student Texts 61. Cambridge: Cambridge University Press.
  • Goodearl, K. R., Yakimov, M. T. (2016). From quantum Ore extensions to quantum tori via noncommutative UFDs. Adv. Math 300:672–716. DOI:10.1016/j.aim.2016.03.029.
  • Goodearl, K. R., Yakimov, M. (2017). Quantum cluster algebra structures on quantum nilpotent algebras. Mem. AMS. 247(1169):0–119. DOI:10.1090/memo/1169.
  • Horton, K. L. (2003). The prime and primitive spectra of multiparameter quantum symplectic and euclidean spaces. Commun. Algebra 31:2713–2743.
  • Jordan, D. A. (1975). Noetherian Ore extensions and Jacobson rings. J. London Math. Soc. 10:281–291. DOI:10.1112/jlms/s2-10.3.281.
  • Krause, G. R., Lenagan, T. H. (2000). Growth of Algebras and Gelfand–Kirillov Dimension, Graduate Studies in Mathematics, 22. Providence, RI: American Mathematical Society.
  • Launois, S. (2003). Idéaux premiers H-invariants de l’algèbre des matrices quantiques, Thèse de Doctorat, Université de Reims.
  • Launois, S., Lenagan, T. H., Rigal, L. (2006). Quantum unique factorisation domains. J. London Math. Soc. 74(02):321–340. DOI:10.1112/S0024610706022927.
  • Launois, S., Lenagan, T. H., Rigal, L. (2008). Prime ideals in the quantum Grassmannian. Sel. Math, New. Ser. 13(4):697–725. DOI:10.1007/s00029-008-0054-z.
  • Lenagan, T. H., Rigal, L. (2003). The maximal order property for quantum determinantal ideals. Proc. Edinburgh Math Soc. 46(3):513–529. DOI:10.1017/S0013091502000809.
  • Lorenz, M. (1984). On the transcendence degree of group algebras of nilpotent groups. Glasgow Math. J. 25(02):167–174. DOI:10.1017/S0017089500005589.
  • McConnell, J. C., Pettit, J. C. (1988). Crossed products and multiplicative analogues of Weyl algebras. J. London Math. Soc. 38:47–55. DOI:10.1112/jlms/s2-38.1.47.
  • Oh, S.-Q. (1997). Catenarity in a class of iterated skew polynomial rings. Commun. Algebra 25(1):37–49. DOI:10.1080/00927879708825838.
  • Tauvel, P. (1978). Sur les quotients premiers de l’algèbre enveloppante d’un algèbre de Lie résoluble. Bull. Soc. Math. France 106:177–205. DOI:10.24033/bsmf.1869.
  • Yakimov, M. (2013). A proof of the Goodearl–Lenagan polynormality conjecture. Int. Math. Res. Notices 2013(9):2097–2132. DOI:10.1093/imrn/rns111.
  • Yakimov, M. (2013). Spectra and catenarity of multi-parameter quantum Schubert cells. Glasgow Math. J. 55A:169–194. DOI:10.1017/S0017089513000578.
  • Zhang, J. J. (1996). On Gelfand–Kirillov transcendence degree. Trans. Amer. Math. Soc. 348(07):2867–2899. DOI:10.1090/S0002-9947-96-01702-3.
  • Zhang, J. J. (1998). On lower transcendence degree. Adv. Math 139(2):157–193. DOI:10.1006/aima.1998.1749.

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