| Title | PBW bases, non-degeneracy conditions and applications |
| Author(s) | Viktor Levandovskyy |
| Text | PBW bases, non-degeneracy conditions and applications |
| Type | Article in Conference Proceedings |
| Abstract | We establish an explicit criteria (the vanishing of non--degeneracy conditions) for certain noncommutative algebras to have Poincar\'e--Birkhoff--Witt basis.
We study theoretical properties of such $G$--algebras, concluding they are
in some sense "close to commutative". We use the non--degeneracy conditions
for practical study of certain deformations of Weyl algebras, quadratic and
diffusion algebras.
|
| Keywords | Poincare-Birkhoff-Witt basis, Non-commutative Groebner basis, Non-commutative associative algebras, Poincare-Birkhoff-Witt theorem, Diamond Lemma, Filtered-graded transfer |
| Length | 18 |
| ISBN | 0-8218-3415-0/hbk |
| Language | English |
| Series | Fields Institute Communications |
| Volume | 45 |
| Pages | 229-246 |
| Publisher | American Mathematical Society (AMS) |
| Address | Providence, RI, USA |
| Year | 2005 |
| Editor | Ragnar-Olaf Buchweitz and Helmut Lenzing |
| Edition | 0 |
| Translation |
No |
| Refereed |
Yes |
| Book | Representations of algebras and related topics |
| Institution |
The Fields Institute for Research in Mathematical Sciences |
| Sponsors | The Fields Institute |
| Conferencename | ICRA X, 10th international conference on representations of algebras |
