$PBW$-deformations of graded rings
Alessandro Ardizzoni, Paolo Saracco, Drago\c{s} \c{S}tefan
TL;DR
This paper generalizes the classical Poincaré-Birkhoff-Witt Theorem to a broad framework, providing new theoretical insights and applications in the study of graded rings and their deformations.
Contribution
It introduces a very general framework for PBW-deformations of graded rings, extending classical results and exploring new applications and examples.
Findings
Several versions of the PBW Theorem are proved in a broad setting
New applications and examples of PBW-deformations are discussed
The results unify and extend previous work on graded ring deformations
Abstract
We prove in a very general framework several versions of the classical Poincar\'e-Birkhoff-Witt Theorem, which extend results from [BeGi, BrGa, CS, HvOZ, WW]. Applications and examples are discussed in the last part of the paper.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons