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Gelfand-Kirillov dimension of multi-filtered algebras

Published online by Cambridge University Press:  20 January 2009

José Gómez Torrecillas
José Gómez Torrecillas
Affiliation:
Dept. Algebra Facultad de Ciencias, Universidad de Granada, E–18071 Granada, Spain, E-mail address: torrecil@ugr.es
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We consider associative algebras filtered by the additive monoid ℕp. We prove that, under quite general conditions, the study of Gelfand-Kirillov dimension of modules over a multi-filtered algebra R can be reduced to the associated ℕp-graded algebra G(R). As a consequence, we show the exactness of the Gelfand-Kirillov dimension when the multi-filtration is finite-dimensional and G(R) is a finitely generated noetherian algebra. Our methods apply to examples like iterated Ore extensions with arbitrary derivations and “homothetic” automorphisms (e.g. quantum matrices, quantum Weyl algebras) and the quantum enveloping algebra of sl(v + 1)

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 1 , February 1999 , pp. 155 - 168
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

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