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Gelfand-Kirillov dimension of algebras with locally nilpotent derivations

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Abstract

Let R be a finitely generated algebra over a field of characteristic 0 with a locally nilpotent derivation δ ≠ 0. We show that if {ie313-1}, where the invariants {ie313-2} are prime and satisfy a polynomial identity, then {ie313-3}. Furthermore, when R is a domain, the same conclusion holds without the assumption that R is finitely generated. This enables us to obtain a result on skew polynomial rings. These results extend work of Bell and Smoktunowicz on domains with GK dimension in the interval [2, 3).

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Authors and Affiliations

  1. Department of Mathematics, DePaul University, 2320 N. Kenmore Avenue, Chicago, IL, 60614, USA

    Jeffrey Bergen

  2. Faculty of Computer Science, Białystok University of Technology, Wiejska 45A, 15-351, Białystok, Poland

    Piotr Grzeszczuk

Authors
  1. Jeffrey Bergen
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  2. Piotr Grzeszczuk
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Corresponding author

Correspondence to Jeffrey Bergen.

Additional information

The first author was supported by the DePaul University Office of Academic Affairs

The research of the second author was supported by the Polish National Center of Science Grant No. DEC-2011/03/B/ST1/04893

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Bergen, J., Grzeszczuk, P. Gelfand-Kirillov dimension of algebras with locally nilpotent derivations. Isr. J. Math. 206, 313–325 (2015). https://doi.org/10.1007/s11856-015-1152-1

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  • DOI: https://doi.org/10.1007/s11856-015-1152-1

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