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

A. Ya Belov

doi:10.1070/sm2004v195n12abeh000862

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

A. Ya Belov

Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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 language	English
Pages (from-to)	1703-1726
Number of pages	24
Journal	Sbornik Mathematics
Volume	195
Issue number	11
DOIs	https://doi.org/10.1070/sm2004v195n12abeh000862
State	Published - 2004
Externally published	Yes

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abstract = "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.",

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AB - 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.

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

Abstract

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