Pointed Hopf algebras: a guided tour to the liftings-Reference-Cited by-同舟云学术

Pointed Hopf algebras: a guided tour to the liftings

Published:2019-12-11 Issue:supl Volume:53 Page:1-44
ISSN:2357-4100
Container-title:Revista Colombiana de Matemáticas
language:
Short-container-title:rev.colomb.mat

Author:

Angiono Iván,García Iglesias Agustín

Abstract

This article serves a two-fold purpose. On the one hand, it is asurvey about the classification 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 B2.

Publisher

Universidad Nacional de Colombia

Subject

General Mathematics

Reference30 articles.

1. N. Andruskiewitsch, I. Angiono, and F. Rossi Bertone, A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2), Bull. Belg. Math. Soc. Simon Stevin 24 (2017), 15-34.

2. N. Andruskiewitsch, I. Angiono, and I. Heckenberger, On finite GK-dimensional Nichols algebras over abelian groups, arXiv:1606.02521. Mem. Amer. Math. Soc., to appear.

3. N. Andruskiewitsch, I. Angiono, and I. Heckenberger, Liftings of Jordan and super Jordan planes, Proc. Edinb. Math. Soc., II. Ser. 61 (2018), no. 3, 661-672.

4. N. Andruskiewitsch, I. Angiono, and A. García Iglesias, Liftings of Nichols algebras of diagonal type I. Cartan type A, Int. Math. Res. Not. IMRN 9 (2017), 2793-2884.

5. N. Andruskiewitsch, I. Angiono, A. García Iglesias, M. Masuoka, and C. Vay, Lifting via cocycle deformation, J. Pure Appl. Alg. 218 (2014), no. 4, 684-703.

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