Our aim in this paper is to investigate symmetry and reversibility properties for quantum algebras and skew PBW extensions. Under certain conditions we prove that these properties transfer from a ring of coefficients to a quantum algebra or skew PBW extension over this ring. In this way we generalize several results established in the literature and consider algebras which have not been studied before. We illustrate our results with remarkable examples of theoretical physics.Key words: Symmetry; reversibility; quantum algebra; skew Poincaré-Birkhoff-Witt extension.1 Universidad Nacional de Colombia, mareyesv@unal.edu.co, https://orcid.org/0000-0002-5774-0822, Bogotá, Colombia.2 Universidad Nacional de Colombia, jcjaramilloq@unal.edu.co, Orinoquia, Colombia.
Universidad EAFIT
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Symmetry and Reversibility Properties for Quantum Algebras and Skew
Poincaré-Birkhoff-Witt ExtensionsPropiedades de simetría y reversibilidad para álgebras cuánticas y extensiones torcidas de Poincaré-Birkhoff-Witt
ResumenNuestro propósito en este artículo es investigar las propiedades de simetría y reversibilidad para álgebras cuánticas y extensiones PBW torcidas. Bajo ciertas condiciones mostramos que estas propiedades se transfieren de un anillo de coeficientes a un álgebra cuántica o extensión PBW torcida sobre este anillo. De esta manera generalizamos diversos resultados establecidos en la literatura, y los ampliamos a álgebras antes no estudiadas. Ilustramos nuestros resultados con ejemplos destacados de la física teórica.Palabras clave: Simetría; reversibilidad; álgebra cuántica; extensión torcida de Poincaré-Birkhoff-Witt.
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