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CENTRALIZERS IN DOMAINS OF GELFAND–KIRILLOV DIMENSION 2

Published online by Cambridge University Press:  19 October 2004

JASON P. BELL  and
LANCE W. SMALL
JASON P. BELL
Affiliation:
Department of Mathematics, University of Michigan, East Hall, 525 East University Ave., Ann Arbor, MI 48109-1109, USAbelljp@math.lsa.umich.edu
LANCE W. SMALL
Affiliation:
Department of Mathematics, University of California San Diego, La Jolla, CA 92093-0112, USAlwsmall@ucsd.edu
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Abstract

Given an affine domain of Gelfand–Kirillov dimension 2 over an algebraically closed field, it is shown that the centralizer of any non-scalar element of this domain is a commutative domain of Gelfand–Kirillov dimension 1 whenever the domain is not polynomial identity. It is shown that the maximal subfields of the quotient division ring of a finitely graded Goldie algebra of Gelfand–Kirillov dimension 2 over a field $F$ all have transcendence degree 1 over $F$. Finally, centralizers of elements in a finitely graded Goldie domain of Gelfand–Kirillov dimension 2 over an algebraically closed field are considered. In this case, it is shown that the centralizer of a non-scalar element is an affine commutative domain of Gelfand–Kirillov dimension 1.

Keywords

16P90
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 6 , November 2004 , pp. 779 - 785
Copyright
© The London Mathematical Society 2004

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