GK dimension of the relatively free algebra for

被引：0
|
作者：
Machado, Gustavo Grings [1 ]
Koshlukov, Plamen [1 ]
机构：
[1] Univ Estadual Campinas, IMECC, Dept Math, BR-13083859 Campinas, SP, Brazil
来源：
MONATSHEFTE FUR MATHEMATIK | 2014年 / 175卷 / 04期
基金：
巴西圣保罗研究基金会;
关键词：
Gelfand-Kirillov dimension; Relatively free Lie algebras; Generic algebras; POLYNOMIAL-IDENTITIES; LIE-ALGEBRAS; GROWTH;
D O I：
10.1007/s00605-014-0687-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let be the Lie algebra of the traceless matrices over an infinite field of characteristic different from 2, denote by the relatively free (also called universal) algebra of rank in the variety of Lie algebras generated by In this paper we compute the Gelfand-Kirillov dimension of the Lie algebra It turns out that whenever one has In order to compute it we use the explicit form of the Hilbert series of described by Drensky. This result is new for ; the case was dealt with by Bahturin in 1979.
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页码：543 / 553
页数：11
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