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Invariants of domains with finite GK dimension

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Abstract

This paper examines the invariants of automorphisms, derivations, and \(q\)-skew derivations of finitely generated domains with finite GK dimension. We generalize results on centralizers obtained by Bell and Small. We show that if a \(q\)-skew derivation is not algebraic, then the GK dimension of the domain exceeds that of its invariants by at least one. In addition, if the domain has GK dimension less than 3 and the ground field is algebraically closed, then the invariants must be commutative.

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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

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  1. Jeffrey Bergen
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  2. Piotr Grzeszczuk
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Correspondence to Jeffrey Bergen.

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Communicated by A. Constantin.

J. Bergen was supported by the DePaul University Office of Academic Affairs. The research of P. Grzeszczuk 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. Invariants of domains with finite GK dimension. Monatsh Math 179, 191–199 (2016). https://doi.org/10.1007/s00605-015-0735-6

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  • DOI: https://doi.org/10.1007/s00605-015-0735-6

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