Nil algebras with restricted growth. (Q2891994)
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scientific article; zbMATH DE number 6047111
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nil algebras with restricted growth. |
scientific article; zbMATH DE number 6047111 |
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18 June 2012
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nil-algebras
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growth of algebras
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graded algebras
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Gelfand-Kirillov dimension
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Nil algebras with restricted growth. (English)
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\textit{T. H. Lenagan} and \textit{A. Smoktunowicz} constructed, over any countable field, an infinite-dimensional finitely generated nil algebra with Gelfand-Kirillov dimension at most 20 [J. Am. Math. Soc. 20, No. 4, 989-1001 (2007; Zbl 1127.16017)]. In this paper, by refining those methods, the authors construct, over any countable field, an infinite-dimensional finitely generated nil algebra with Gelfand-Kirillov dimension at most 3. In fact, the constructed algebra requires only two generators.
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