Smashed extensions for Hopf algebra \(\text{SL}_q(2)\) (Q1267225)

Let \(R\) be a right comodule algebra over the Hopf algebra \(H\). Then \(R\) is an \(H\)-cleft extension of the subalgebra \(R_0\) of coinvariants if there exists a convolution invertible \(H\)-comodule morphism \(\phi\colon H\to R\) with \(\phi(1)=1\). If moreover \(\phi\) is an algebra map, then \(R\) is called an \(H\)-smashed extension of \(R_0\), which means that \(R_0\) is a left \(H\)-module algebra and \(R\) is isomorphic to the smash product \(R_0\#H\). The aim of the paper is to describe \(\text{SL}_q(2)\)-smashed extensions in terms of \(\text{End}(R_0)\)-points of \(\text{SL}_q(2)\) satisfying a certain property.