Poincare-Birkhoff-Witt Theorems
arXiv:1404.6497
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.
30 pages; survey article to appear in Mathematical Sciences Research Institute Proceedings
References in corpus (11)
- The Weyl-Brandt groupoid of a Nichols algebra of diagonal type
- On the quotient ring by diagonal harmonics
- Nonhomogeneous quadratic duality and curvature
- PBW-deformations of N-Koszul algebras
- Quantum Drinfeld Hecke Algebras
- Representations of Rational Cherednik Algebras in Positive Characteristic
- Quantized symplectic oscillator algebras of rank one
- Poincare-Birkhoff-Witt deformations of smash product algebras from Hopf actions on Koszul algebras
- Drinfeld-Hecke algebras over cocommutative algebras
- Hecke algebras and symplectic reflection algebras
- Poincaré's Proof of the so-called Birkhoff-Witt Theorem