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Primitive Algebras with Arbitrary Gelfand-Kirillov Dimension

✍ Scribed by Uzi Vishne

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
379 KB
Volume
211
Category
Article
ISSN
0021-8693

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✦ Synopsis

We construct, for every real /3 > 2, a primitive affine algebra with Gelfand Kirillov dimension /3. Unlike earlier constructions, there are no assumptions on the base field. In particular, this is the first construction over N or C. Given a recursive sequence {v,} of elements in a free monoid, we investigate the quotient of the free associative algebra by the ideal generated by all nonsubwords in {~Jn}. We bound the dimension of the resulting algebra in terms of the growth of {vn}. In particular, if Ivnl is less than doubly exponential, then the dimension is 2. This also answcrs affirmatively a conjecture of Salwa (1997, Comm. Algebra 25, 3965-3972).

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Let A be a three dimensional Artin᎐Schelter regular algebra. We give a description of the category of finitely generated A-modules of Gelfand᎐Kirillov Ž . dimension one modulo those of finite dimension over the ground field . The proof is based upon a result by Gabriel which says that locally finite