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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn063, 8 pages, doi:10.1093/imrn/rnn063 published on June 13, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Every Quantum Minor Generates an Ore Set

Zoran Skoda

Institute Ruder Boskovic, Division of Theoretical Physics, P.O. Box 180, HR-10002 Zagreb, Croatia

Correspondence: Correspondence to be sent to: Zoran Skoda, Institute Ruder Boskovic, Division of Theoretical Physics, P.O. Box 180, HR-10002 Zagreb, Croatia. E-mail: zskoda{at}irb.hr

The subset multiplicatively generated by any given set of quantum minors, and the unit element in the quantum matrix bialgebra satisfies the left and right Ore conditions.



References

  1. Artin M., Schelter W., Tate J. Quantum Deformations of GLn. Communications on Pure and Applied Mathematics (1991) 44(8-9):879–95.[CrossRef][ISI]
  2. Beilinson A., Bernstein J. Localization de G-modules. Comptes Rendus Mathématiques des l'Académie des Sciences (1981) 292:15–8.
  3. Demidov E. E. "Multiparameter quantum deformations of the group GL(n)" [in Russian]. Uspehi Mat. Nauk (1991) 46(4):147–8. Russian Mathematical Surveys 46, no. 4 (1991): 169–71.
  4. Fioresi R. Commutation relations among generic quantum minors in Oq(Mn(k)). Journal of Algebra (2004) 280(2):655–82.[CrossRef][ISI]
  5. Hashimoto M., Hayashi T. Quantum multilinear algebra. Tôhoku Mathematical Journal (1992) 44:471–521.[CrossRef][ISI]
  6. Joseph A. Faithfully Flat Embeddings for Minimal Primitive Quotients of Quantized Enveloping Algebras. Quantum Deformations of alg-s and Their rep-s—Joseph A., Shnider S., eds. (1993) Ramat Gan, Israel: Bar Ilan University. 79–106. Israel Mathematics Conference Proceedings 7.
  7. Krob D., Leclerc B. Minor identities for quasi-determinants and quantum determinants. Communications in Mathematical Physics (1995) 169:1–23.[CrossRef][ISI]
  8. Lunts V. A., Rosenberg A. L. Differential operators on noncommutative rings. (1997) 335–59. Selecta Math. 3.
  9. Lunts V. A., Rosenberg A. L. Localization for quantum groups (1999) (1):123–59. Selecta Math. 5.
  10. Manin Yu. I. Quantum Groups and Non-commutative Geometry (1988) Montreal, ON, Canada: Université de Montréal, Centre de Recherches Mathématiques.
  11. Manin Yu. I. Multiparametric quantum deformation of the general linear supergroup. Communications in Mathematical Physics (1989) 123:163–75.[CrossRef][ISI]
  12. Parshall B., Wang J. Quantum Linear Groups (1991) Providence, RI: American Mathematical Society. Memoirs of the American Mathematical Society 439.
  13. Reshetikhin N. Yu., Takhtajan L. A., Faddeev L. D. "Quantization of Lie groups and Lie algebras" [in Russian]. In: Algebra i analiz (1989) 1:178.
  14. Rosenberg A. L. Noncommutative schemes. Compositio Mathematicae (1998) 112:93–125.[CrossRef]
  15. Skoda Z. Included-row exchange principle for quantum minors. (2005) preprint math.QA/0510512.
  16. Skoda Z. Localizations for Construction of Quantum Coset Spaces. In: Noncommutative Geometry and Quantum Groups—Hajac P. M., Pusz W., eds. (2003) Warszawa, Poland: Polish Academy of Sciences. 265–98. Banach Center Publications 61.
  17. Skoda Z. Coherent states for Hopf algebras. Letters in Mathematical Physics (2007) 81(1):1–17.[CrossRef][ISI]
  18. Skoda Z. The geometric meaning of quantum Gauss decomposition. (forthcoming).
  19. Skoda Z. A simple algorithm for extending the identities for quantum minors to multiparametric case. (2008) preprint arXiv:0801.4965.
  20. Skoda Z. Noncommutative Localization in Noncommutative Geometry. In: Noncommutative Localization in Topology and Algebra—Ranicki A., ed. (2006) Cambridge, United Kingdom: Cambridge University Press. 220–313. London Mathematical Society Lecture Note Series 330.
  21. Tanisaki T. The Beilinson-Bernstein correspondence for quantized enveloping algebras. Mathematische Zeitschrift (2005) 250(2):299–361.[CrossRef][ISI]
  22. van Oystaeyen F. Algebraic geometry for associative algebras. (2000) New York: Marcel Dekker.

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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
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Right arrow Email this article to a friend
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