An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension

Lenagan, T.; Smoktunowicz, Agata

doi:10.1090/S0894-0347-07-00565-6

An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension
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by T. H. Lenagan and Agata Smoktunowicz

J. Amer. Math. Soc. 20 (2007), 989-1001

DOI: https://doi.org/10.1090/S0894-0347-07-00565-6

Published electronically: April 2, 2007

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Abstract:

The famous 1960’s construction of Golod and Shafarevich yields infinite dimensional nil, but not nilpotent, algebras. However, these algebras have exponential growth. Here, we construct an infinite dimensional nil, but not locally nilpotent, algebra which has polynomially bounded growth.

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