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Type: Artigo de periódico
Title: Gk Dimension Of The Relatively Free Algebra For Sl2
Author: Machado G.G.
Koshlukov P.
Abstract: Let sl2(K) be the Lie algebra of the 2 × 2 traceless matrices over an infinite field K of characteristic different from 2, denote by Rm = Rm(sl2(K)) the relatively free (also called universal) algebra of rankm in the variety of Lie algebras generated by sl2(K). In this paper we compute the Gelfand-Kirillov dimension of the Lie algebra Rm(sl2(K)). It turns out that whenever m ≥ 2 one has GK dim Rm = 3(m − 1). In order to compute it we use the explicit form of the Hilbert series of Rm described by Drensky. This result is new for m > 2; the case m = 2 was dealt with by Bahturin in 1979.
Editor: Springer-Verlag Wien
Rights: fechado
Identifier DOI: 10.1007/s00605-014-0687-2
Date Issue: 2014
Appears in Collections:Unicamp - Artigos e Outros Documentos

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