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Journal of the London Mathematical Society 2000 62(2):370-380; doi:10.1112/S0024610700001083
© 2000 by London Mathematical Society
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© The London Mathematical Society

Poincaré Series of Multi-Filtered Algebras and Partitivity

J. Gómez Torrecillas and T. H. Lenagan

Departamento de Algebra, Facultad de Ciencias, Universidad de Granada E-18071 Granada, Spain, torrecil{at}ugr.es
Department of Mathematics, University of Edinburgh James Clerk Maxwell Building, Kings Buildings, Mayfield Road, Edinburgh EH9 3JZ, tom{at}mathematics.edinburgh.ac.uk

Received 2 September 1998. Revision received 27 October 1999.

It is proved that if an algebra R over a field can be endowed with a pointed and finite-dimensional Nn-filtration such that the associated Nn-graded algebra T is semi-commutative, then R is left and right finitely partitive. In order to do this, a multi-variable Poincaré series for every finitely generated graded T-module is considered and it is shown that this Poincaré series is a rational function. The methods apply to some iterated Ore extensions such as quantum matrices and quantum Weyl algebras as well as to the quantized enveloping algebra of sl({nu}+1).


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