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GK DIMENSION AND LOCALLY NILPOTENT SKEW DERIVATIONS

Part of: Rings and algebras with additional structure Chain conditions, growth conditions, and other forms of finiteness

Published online by Cambridge University Press:  18 December 2014

JEFFREY BERGEN  and
PIOTR GRZESZCZUK
JEFFREY BERGEN
Affiliation:
Department of Mathematics DePaul University 2320 N. Kenmore Avenue, Chicago, Illinois 60614, USA e-mail: jbergen@depaul.edu
PIOTR GRZESZCZUK
Affiliation:
Faculty of Computer Science, Białystok University of Technology, Wiejska 45A, 15-351 Białystok, Poland e-mail: piotrgr@pb.edu.pl
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Abstract

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Let A be a domain over an algebraically closed field with Gelfand–Kirillov dimension in the interval [2,3). We prove that if A has two locally nilpotent skew derivations satisfying some natural conditions, then A must be one of five algebras. All five algebras are Noetherian, finitely generated, and have Gelfand–Kirillov dimension equal to 2. We also obtain some results comparing the Gelfand–Kirillov dimension of an algebra to its subring of invariants under a locally nilpotent skew derivation.

MSC classification

Primary: 16P90: Growth rate, Gelfand-Kirillov dimension
Secondary: 16W25: Derivations, actions of Lie algebras
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 3 , September 2015 , pp. 555 - 567
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

References

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