The Gel'fand-Kirillov dimension of relatively free associative algebras

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In this paper the Gel'fand-Kirillov dimension GKdim(A) is calculated for a relatively free associative algebra A over an arbitrary ground field. This dimension is determined by the complexity type of the algebra A or by the set of semidirect products of matrix algebras over a polynomial ring contained in the variety Var(A). The proof is comparatively elementary and does not use the local representability of relatively free algebras.

Original languageEnglish
Pages (from-to)1703-1726
Number of pages24
JournalSbornik Mathematics
Issue number11
StatePublished - 2004
Externally publishedYes


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