Please use this identifier to cite or link to this item: http://repositorio.unicamp.br/jspui/handle/REPOSIP/326365
Type: Artigo
Title: Gk-dimension Of 2 X 2 Generic Lie Matrices
Author: Drensky
Vesselin; Koshlukov
Plamen; Machado
Gustavo Grings
Abstract: Recently Machado and Koshlukov have computed the Gelfand Kirillov dimension of the relatively free algebra F-m = F-m(var (sl(2)(K))) of rank m in the variety of algebras generated by the three-dimensional simple Lie algebra sl2 (K) over an infinite field K of characteristic different from 2. They have shown that GKdim(F-m) = 3(m-1). The algebra F-m is isomorphic to the Lie algebra generated by m generic 2 x 2 matrices. Now we give a new proof for GKdim(F-m) using classical results of Procesi and Razmyslov combined with the observation that the commutator ideal of F-m is a module of the center of the associative algebra generated by m generic traceless 2 x 2 matrices.
Subject: Gelfand Kirillov Dimension
Generic Matrices
Matrix Invariants
Relatively Free Lie Algebras
Editor: Kossuth Lajos Tudomanyegyetem
Debrecen
Rights: fechado
Identifier DOI: 10.5486/PMD.2016.7400
Address: http://www.math.unideb.hu/publi/contents.php?szam=89
Date Issue: 2016
Appears in Collections:Unicamp - Artigos e Outros Documentos

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