Finite generation of division subalgebras and of the group of eigenvalues for commuting derivations or automorphisms of division algebras
| dc.creator | Bavula, V. V. | |
| dc.date | 2005-05-06 | |
| dc.date.accessioned | 2026-07-07T05:19:41Z | |
| dc.date.available | 2026-07-07T05:19:41Z | |
| dc.description | Let $D$ be a division algebra such that $D\t D^o$ is a Noetherian algebra, then any division subalgebra of $D$ is a {\em finitely generated} division algebra. Let $\D $ be a finite set of commuting derivations or automorphisms of the division algebra $D$, then the group $\Ev (\D)$ of common eigenvalues (i.e. {\em weights}) is a {\em finitely generated abelian} group. Typical examples of $D$ are the quotient division algebra ${\rm Frac} (\CD (X))$ of the ring of differential operators $\CD (X)$ on a smooth irreducible affine variety $X$ over a field $K$ of characteristic zero, and the quotient division algebra ${\rm Frac} (U (\Gg))$ of the universal enveloping algebra $U(\Gg)$ of a finite dimensional Lie algebra $\Gg $. It is proved that the algebra of differential operators $\CD (X)$ is isomorphic to its opposite algebra $\CD (X)^o$. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505116 | |
| dc.identifier | http://arxiv.org/abs/math/0505116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75106 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16S15, 16W25, 16S32, 16P40, 16K40 | |
| dc.title | Finite generation of division subalgebras and of the group of eigenvalues for commuting derivations or automorphisms of division algebras | |
| dc.type | text |