Combinatorial aspects of normal ordering of 3-dimensional skew polynomial rings
Andr\'es Rubiano, Armando Reyes
TL;DR
This paper explores the combinatorial properties of normal ordering in 3D skew polynomial rings, utilizing SageMath to optimize computations of PBW forms and algebraic commutation rules.
Contribution
It introduces computational techniques to efficiently determine PBW forms and normal orderings in 3D skew polynomial rings, enhancing previous methods.
Findings
Reduced computation time for PBW forms using SageMath
Improved understanding of normal ordering in skew polynomial rings
Classified 3D skew polynomial rings by Bell and Smith
Abstract
In this paper, we discuss combinatorial aspects of normal ordering of 3-dimensional skew polynomial rings defined and classified by Bell and Smith \cite{BellSmith1990}. With some help of the Mathematical software \texttt{SageMath}, we are able to reduce the length of computation of PBW forms and normal orderings appearing in commutation rules of these algebras.
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