Division algebras of Gelfand-Kirillov dimension two
| dc.creator | Bell, Jason P. | |
| dc.date | 2007-02-05 | |
| dc.date | 2007-08-20 | |
| dc.date.accessioned | 2026-07-07T08:24:31Z | |
| dc.date.available | 2026-07-07T08:24:31Z | |
| dc.description | 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. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702119 | |
| dc.identifier | http://arxiv.org/abs/math/0702119 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136364 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16P90 | |
| dc.title | Division algebras of Gelfand-Kirillov dimension two | |
| dc.type | text |