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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.53 supl.1 Bogotá Dec. 2019 Epub Mar 24, 2020
https://doi.org/10.15446/recolma.v53nsupl.83958
Artículos originales
Pointed Hopf algebras: a guided tour to the liftings
Álgebras de Hopf punteadas: una excursión a los levantamientos
1 Universidad Nacional de Córdoba, Argentina
2 Universidad Nacional de Córdoba, Argentina
This article serves a two-fold purpose. On the one hand, it is a survey about the classi cation of finite-dimensional pointed Hopf algebras with abelian coradical, whose final step is the computation of the liftings or deformations of graded Hopf algebras. On the other, we present a step-by-step guide to carry out the strategy developed to construct the liftings. As an example, we conclude the work with the classification of pointed Hopf algebras of Cartan type B 2.
Keywords: Hopf algebras; Liftings; Cleft objetcs
Este artículo tiene un doble propósito. Por un lado, repasamos la clasificación de las álgebras de Hopf punteadas de dimensión finita con corradical abeliano, cuyo paso final es el cálculo de los levantamientos o deformaciones de álgebras de Hopf graduadas. Por otro, presentamos una guía paso a paso para llevar a cabo la estrategia desarrollada para construir los levantamientos. Concluimos el trabajo con un ejemplo donde damos la clasificación de las álgebras de Hopf punteadas de tipo Cartan B 2.
Palabras clave: Álgebras de Hopf; Levantamientos; Objetos hendidos
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Received: June 15, 2018; Accepted: November 16, 2018
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