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Division algebras of Gelfand-Kirillov transcendence degree 2

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Abstract

Let A be a finitely generated K-algebra that is a domain of GK dimension less than 3, and let Q(A) denote the quotient division algebra of A. We show that if D is a division subalgebra of Q(A) of GK dimension at least 2, then Q(A) is finite dimensional as a left D-vector space. We use this to show that if A is a finitely generated domain of GK dimension less than 3 over an algebraically closed field K, then any division subalgebra D of Q(A) is either a finitely generated field extension of K of transcendence degree at most one, or Q(A) is finite dimensional as a left D-vector space.

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Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC, V5A 1S6, Canada

    Jason P. Bell

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  1. Jason P. Bell
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Correspondence to Jason P. Bell.

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The author thanks NSERC for its generous support.

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Bell, J.P. Division algebras of Gelfand-Kirillov transcendence degree 2. Isr. J. Math. 171, 51–60 (2009). https://doi.org/10.1007/s11856-009-0039-4

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  • DOI: https://doi.org/10.1007/s11856-009-0039-4

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