Title  PBW bases, nondegeneracy conditions and applications 
Author(s)  Viktor Levandovskyy 
Text  PBW bases, nondegeneracy conditions and applications 
Type  Article in Conference Proceedings 
Abstract  We establish an explicit criteria (the vanishing of nondegeneracy conditions) for certain noncommutative algebras to have Poincar\'eBirkhoffWitt basis.
We study theoretical properties of such $G$algebras, concluding they are
in some sense "close to commutative". We use the nondegeneracy conditions
for practical study of certain deformations of Weyl algebras, quadratic and
diffusion algebras.

Keywords  PoincareBirkhoffWitt basis, Noncommutative Groebner basis, Noncommutative associative algebras, PoincareBirkhoffWitt theorem, Diamond Lemma, Filteredgraded transfer 
Length  18 
ISBN  0821834150/hbk 
Language  English 
Series  Fields Institute Communications 
Volume  45 
Pages  229246 
Publisher  American Mathematical Society (AMS) 
Address  Providence, RI, USA 
Year  2005 
Editor  RagnarOlaf 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 