Vol. 252, No. 1, 2011

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On pointed Hopf algebras over dihedral groups

Fernando Fantino and Gaston Andrés Garcia

Vol. 252 (2011), No. 1, 69–91
Abstract

Let 𝔻m be the dihedral group of order 2m with m = 4t, t 3. Given an algebraically closed field of characteristic 0, we classify all finite-dimensional Nichols algebras over 𝔻m and all finite-dimensional pointed Hopf algebras whose group of group-likes is 𝔻m, by means of the lifting method. As a byproduct we obtain new examples of finite-dimensional pointed Hopf algebras.

Keywords
pointed Hopf algebra, Nichols algebra, dihedral group
Mathematical Subject Classification 2000
Primary: 16W30, 16T05, 17B37
Milestones
Received: 5 July 2010
Accepted: 7 December 2010
Published: 8 October 2011

Proposed: Vyjayanthi Chari
Authors
Fernando Fantino
Universidad Nacional de Córdoba
Facultad de Matemática, Astronomía y Física - CIEM
Medina Allende s/n
Ciudad Universitaria
5000 Córdoba
Argentina
http://www.famaf.unc.edu.ar/~fantino/
Gaston Andrés Garcia
Universidad Nacional de Córdoba
Facultad de Matemática, Astronomía y Física - CIEM
Medina Allende s/n
Ciudad Universitaria
5000 Córdoba
Argentina
http://www.famaf.unc.edu.ar/~ggarcia/