Gelfand-Kirillov dimension for automorphism groups of relatively free algebras (Q2711607)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gelfand-Kirillov dimension for automorphism groups of relatively free algebras |
scientific article |
Statements
2 July 2001
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growth functions
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Gelfand-Kirillov dimension
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relatively free algebras
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automorphism groups
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varieties of algebras
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tame automorphisms
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Gelfand-Kirillov dimension for automorphism groups of relatively free algebras (English)
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Let \(K\) be a field of characteristic 0, and let \(F_n(V)\) be the relatively free algebra of rank \(n\) in the variety \(V\). The authors introduce a certain growth function, and study the corresponding Gelfand-Kirillov dimension. They provide some (quite natural) conditions for coincidence of the Gelfand-Kirillov dimensions of the group of all tame automorphisms of \(F_n(V)\) and of the algebra \(F_n(V)\). Further they compute the GK-dimensions of the automorphism groups of \(F_n(V)\) for several important varieties, and show that in some cases the GK-dimension of the group of tame automorphisms of \(F_n(V)\) is strictly less than that of the group of all automorphisms of \(F_n(V)\).
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