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Nil algebras with restricted growth

  • T. H. Lenagan (a1), Agata Smoktunowicz (a1) and Alexander A. Young (a2)


It is shown that over an arbitrary countable field there exists a finitely generated algebra that is nil, infinite dimensional and has Gelfand–Kirillov dimension at most 3.



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1.Golod, E. S., On nil-algebras and finitely approximable p-groups, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 273276 (in Russian).
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3.Gromov, M., Groups of polynomial growth and expanding maps, Publ. Math. IHES 53 (1981), 5373.
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10.Zelmanov, E., Some open problems in the theory of infinite dimensional algebras, J. Korean Math. Soc. 44 (2007), 11851195.


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