Abstract
It is shown here that, for a number of quantum groups, there exists a finite dimensional ‘filtration’ for which the associated graded algebra has a simple form. It follows from this that Gelfand-Kirillov dimension behaves particularly well for these algebras.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Humphreys, J.E. Introduction to Lie algebras and representation theory. Graduate Texts No. 9. Springer Verlag, New York-Berlin, 1972.
Kac, V. Infinite dimensional Lie algebras, 2nd ed. Cambridge University Press, Cambridge-New York, 1985.
Lorenz, M. Gelfand-Kirillov dimension and Poincaré series. Cuadernos de Algebra No. 7. Universidad de Granada, 1988, pp. 68.
Lusztig, G. Canonical bases arising from quantized enveloping algebras. Preprint, M.I.T., 1989.
McConnell, J.C. and Pettit, J.J. Crossed products and multiplicative analogues of Weyl algebras. J. London Math. Soc. 38 (1988) 47–55.
McConnell, J.C. and Robson, J.C. Noncommutative Noetherian rings. J. Wiley and Sons, Chichester-New York, 1987.
McConnell, J.C. and Stafford, J.T. Gelfand-Kirillov dimension and associated graded modules. J. Algebra 125 (1989) 197–214.
Manin, Yu. I. Quantum group and non-commutative geometry. Les. Publ. du Centre de Récherches Math. Université de Montreal, 1988.
Smith, S.P. Quantum groups: An introduction and survey for ring theorists. Preprint, University of Washington, Seattle, 1989.
Takeuchi, M. The q-bracket product and the P.B.W. theorem for quantum enveloping algebras of classical types (A n ), (B n ), (C n ) and (D n ). Preprint, University of Tsukuba, 1989.
Yamane, H. A P.B.W. theorem for quantized universal enveloping algebras of type A n . Publ. R.I.M.S. Kyoto 25 (1989) 503–520.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag
About this paper
Cite this paper
McConnell, J.C. (1990). Quantum groups, filtered rings and Gelfand-Kirillov dimension. In: Jain, S.K., López-Permouth, S.R. (eds) Non-Commutative Ring Theory. Lecture Notes in Mathematics, vol 1448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091258
Download citation
DOI: https://doi.org/10.1007/BFb0091258
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53164-7
Online ISBN: 978-3-540-46745-8
eBook Packages: Springer Book Archive