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 |