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Original Articles

Gelfand–Kirillov dimension of generalized Weyl algebras (In memory of Guenter Rudolf Krause (1941–2015))

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Pages 4403-4413 | Received 23 Jun 2017, Published online: 19 Mar 2018
 

ABSTRACT

Given a generalized Weyl algebra A of degree 1 with the base algebra D, we prove that the difference of the Gelfand–Kirillov dimension of A and that of D could be any positive integer or infinity. Under mild conditions, this difference is exactly 1. As applications, we calculate the Gelfand–Kirillov dimensions of various algebras of interest, including the (quantized) Weyl algebras, ambiskew polynomial rings, noetherian (generalized) down-up algebras, iterated Ore extensions, quantum Heisenberg algebras, universal enveloping algebras of Lie algebras, quantum GWAs, etc.

2010 MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgment

The authors would like to thank the anonymous referee for his/her useful comments and suggestions.

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