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|Type:||Artigo de periódico|
|Title:||Gk Dimension Of The Relatively Free Algebra For Sl2|
|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.|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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