Poincare-Birkhoff-Witt Theorems
Rings and Algebras
2014-04-28 v1 Representation Theory
Abstract
We sample some Poincare-Birkhoff-Witt theorems appearing in mathematics. Along the way, we compare modern techniques used to establish such results, for example, the Composition-Diamond Lemma, Groebner basis theory, and the homological approaches of Braverman and Gaitsgory and of Polishchuk and Positselski. We discuss several contexts for PBW theorems and their applications, such as Drinfeld-Jimbo quantum groups, graded Hecke algebras, and symplectic reflection and related algebras.
Cite
@article{arxiv.1404.6497,
title = {Poincare-Birkhoff-Witt Theorems},
author = {Anne V. Shepler and Sarah Witherspoon},
journal= {arXiv preprint arXiv:1404.6497},
year = {2014}
}
Comments
30 pages; survey article to appear in Mathematical Sciences Research Institute Proceedings