Primitive algebraic algebras of polynomially bounded growth

Jason P. Bell; Lance W. Small; Agata Smoktunowicz

doi:10.1090/conm/562/11129

Primitive algebraic algebras of polynomially bounded growth

Jason P. Bell, Lance W. Small, Agata Smoktunowicz

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We show that if $k$ is a countable field, then there exists a finitely generated, infinite-dimensional, primitive algebraic $k$-algebra $A$ whose Gelfand-Kirillov dimension is at most six. In addition to this we construct a two-generated primitive algebraic $k$-algebra. We also pose many open problems.

Original language	English
Title of host publication	New Trends in Noncommutative Algebra
Subtitle of host publication	A Conference in Honor of Ken Goodearl’s 65th Birthday
Editors	P Ara, K. A. Brown, T. H. Lenagan, E. S. Letzter, J. T. Stafford, J. J. Zhang
Publisher	American Mathematical Society
Number of pages	12
Volume	562
ISBN (Electronic)	978-0-8218-8497-3
ISBN (Print)	978-0-8218-5297-2
DOIs	https://doi.org/10.1090/conm/562/11129
Publication status	Published - 2012

Keywords

math.RA

Access to Document

10.1090/conm/562/11129

Primitive algebraic algebras of polynomially bounded growthAccepted author manuscript, 623 KB

http://www.ams.org/books/conm/562/

Nil algebras, algebraic algebras and algebras with finite Gelfand-Kirillov dimension
Smoktunowicz, A.
EPSRC
1/08/06 → 31/07/11
Project: Research

Cite this

P. Bell, J., W. Small, L., & Smoktunowicz, A. (2012). Primitive algebraic algebras of polynomially bounded growth. In P. Ara, K. A. Brown, T. H. Lenagan, E. S. Letzter, J. T. Stafford, & J. J. Zhang (Eds.), New Trends in Noncommutative Algebra: A Conference in Honor of Ken Goodearl’s 65th Birthday (Vol. 562). American Mathematical Society. https://doi.org/10.1090/conm/562/11129

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abstract = "We show that if $k$ is a countable field, then there exists a finitely generated, infinite-dimensional, primitive algebraic $k$-algebra $A$ whose Gelfand-Kirillov dimension is at most six. In addition to this we construct a two-generated primitive algebraic $k$-algebra. We also pose many open problems.",

keywords = "math.RA",

author = "{P. Bell}, Jason and {W. Small}, Lance and Agata Smoktunowicz",

note = "11 pages (pages 41--52)",

year = "2012",

doi = "10.1090/conm/562/11129",

language = "English",

isbn = "978-0-8218-5297-2",

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booktitle = "New Trends in Noncommutative Algebra",

publisher = "American Mathematical Society",

address = "United States",

}

Primitive algebraic algebras of polynomially bounded growth. / P. Bell, Jason; W. Small, Lance; Smoktunowicz, Agata.

New Trends in Noncommutative Algebra: A Conference in Honor of Ken Goodearl’s 65th Birthday. ed. / P Ara; K. A. Brown; T. H. Lenagan; E. S. Letzter; J. T. Stafford; J. J. Zhang. Vol. 562 American Mathematical Society, 2012.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Primitive algebraic algebras of polynomially bounded growth

AU - P. Bell, Jason

AU - W. Small, Lance

AU - Smoktunowicz, Agata

N1 - 11 pages (pages 41--52)

PY - 2012

Y1 - 2012

N2 - We show that if $k$ is a countable field, then there exists a finitely generated, infinite-dimensional, primitive algebraic $k$-algebra $A$ whose Gelfand-Kirillov dimension is at most six. In addition to this we construct a two-generated primitive algebraic $k$-algebra. We also pose many open problems.

AB - We show that if $k$ is a countable field, then there exists a finitely generated, infinite-dimensional, primitive algebraic $k$-algebra $A$ whose Gelfand-Kirillov dimension is at most six. In addition to this we construct a two-generated primitive algebraic $k$-algebra. We also pose many open problems.

KW - math.RA

U2 - 10.1090/conm/562/11129

DO - 10.1090/conm/562/11129

M3 - Conference contribution

SN - 978-0-8218-5297-2

VL - 562

BT - New Trends in Noncommutative Algebra

A2 - Ara, P

A2 - Brown, K. A.

A2 - Lenagan, T. H.

A2 - Letzter, E. S.

A2 - Stafford, J. T.

A2 - Zhang, J. J.

PB - American Mathematical Society

ER -

Primitive algebraic algebras of polynomially bounded growth

Abstract

Keywords

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Projects

Nil algebras, algebraic algebras and algebras with finite Gelfand-Kirillov dimension

Cite this