2014/04/25 by Anne V. Shepler, Shepler, Anne V., Sarah Witherspoon +1
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT
paper · pdf · doi:10.48550/arxiv.1404.6497
30 pages; survey article to appear in Mathematical Sciences Research Institute Proceedings
arxiv created 2014/04/25 · arxiv updated 2014/04/28
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.