Primitive algebras with arbitrary Gelfand-Kirillov dimension

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We construct, for every real β≥2, a primitive affine algebra wi th Gelfand-Kirillov dimension β. Unlike earlier constructions, there are no assumptions on the base field. In particular, this is the first construction over R or C. Given a recursive sequence {vn} of elements in a free monoid, we investigate the quotient of the free associative algebra by the ideal generated by all nonsubwords in {vn}. We bound the dimension of the resulting algebra in terms of the growth of {vn}. In particular, if {vn} is less than doubly exponential, then the dimension is 2. This also answers affirmatively a conjecture of Salwa (1997,Comm. Algebra25, 3965-3972).

Original languageEnglish
Pages (from-to)150-158
Number of pages9
JournalJournal of Algebra
Issue number1
StatePublished - 1 Jan 1999


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