Right coideal subalgebras of a bosonization of the Fomin–Kirillov algebra FK3

Abstract

In this work we explicitly calculate all the right coideal subalgebras of the Hopf algebra $\mathcal{H}$ which is the bosonization of the Fomin–Kirillov algebra $\mathcal{F}{\mathcal{K}}_3$ over the symmetric group ${\mathbb{S}}_3.$ First we consider the case of right coideal subalgebras containing the coradical $\mathbb{k}{\mathbb{S}}_3.$ Then we also describe the objects that do not contain the coradical, completing the classification.

Keywords:

• Coideal subalgebra
• Hopf algebras
• Nichols algebras

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 57T05
• 16T15

Acknowledgments

We thank Nicolás Andruskiewitsch for interesting discussions on this topic. We also thank him for his constant support and motivation.

Additional information

Funding

The first author was partially supported by CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior).