Division algebras of Gelfand-Kirillov dimension two

Details Division algebras of Gelfand-Kirillov dimension two Division algebras of Gelfand-Kirillov dimension two

2007-02-05

arxiv.org/abs/math/0702119v2

Mathematics

Rings and Algebras

9 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Division algebras of Gelfand-Kirillov dimension two does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Division algebras of Gelfand-Kirillov dimension two, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Division algebras of Gelfand-Kirillov dimension two will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-427295