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Nil algebras with restricted growth

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

Abstract

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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References

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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.
4.Krause, G. R. and Lenagan, T. H., Growth of algebras and Gelfand–Kirillov dimension Graduate Studies in Mathematics, Volume 22, Revised Edition (American Mathematical Society, Providence, RI, 2000).
5.Lenagan, T. H. and Smoktunowicz, A., An infinite dimensional algebra with finite Gelfand–Kirillov algebra, J. Am. Math. Soc. 20 (2007), 9891001.
6.Small, L. W., Stafford, J. T. and Warfield, R. B. Jr, Affine algebras of Gelfand–Kirillov dimension one are PI, Math. Proc. Camb. Phil. Soc. 97 (1985), 407414.
7.Smoktunowicz, A., Polynomial rings over nil rings need not be nil, J. Alg. 233 (2000), 427436.
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9.Ufnarovskij, V. A., Combinatorial and asymptotic methods in algebra, in Algebra VI, Encyclopaedia of Mathematical Sciences, Volume 57, pp. 1196 (Springer, 1995).
10.Zelmanov, E., Some open problems in the theory of infinite dimensional algebras, J. Korean Math. Soc. 44 (2007), 11851195.

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