TY - JOUR

T1 - Primitive algebras with arbitrary Gelfand-Kirillov dimension

AU - Vishne, Uzi

PY - 1999/1/1

Y1 - 1999/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=0032622835&partnerID=8YFLogxK

U2 - 10.1006/jabr.1998.7567

DO - 10.1006/jabr.1998.7567

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AN - SCOPUS:0032622835

SN - 0021-8693

VL - 211

SP - 150

EP - 158

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -