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 -