Rotational Symmetries in Polynomial Rings
Keith Conrad, Ambar N. Sengupta
TL;DR
This paper investigates how rotation generators act on polynomials over commutative rings and explores harmonic polynomials within an algebraic framework, providing new insights into their structure and symmetries.
Contribution
It introduces algebraic descriptions of rotational symmetries and harmonic polynomials in polynomial rings, expanding understanding of their algebraic properties.
Findings
Characterization of rotation actions on polynomial rings
Algebraic properties of harmonic polynomials
New results on symmetry behavior in polynomial algebra
Abstract
We obtain results describing the behavior of the action of rotation generators on polynomials over a commutative ring. We also explore harmonic polynomials in a purely algebraic setting.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Nonlinear Waves and Solitons · Advanced Topics in Algebra