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|Title:||Gk-dimension Of 2 X 2 Generic Lie Matrices|
|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|
Relatively Free Lie Algebras
|Editor:||Kossuth Lajos Tudomanyegyetem|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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