A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)
A finite-dimensional Lie algebra arising from a Nichols algebra of diagonal type (rank 2)
Let ${\mathcal{B}}_{\mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type corresponding to a matrix $\mathfrak{q} \in {\mathbf{k}}^{\theta \times \theta}$. Let ${\mathcal{L}}_{\mathfrak{q}}$ be the Lusztig algebra associated to ${\mathcal{B}}_{\mathfrak{q}}$. We present ${\mathcal{L}}_{\mathfrak{q}}$ as an extension (as braided Hopf algebras) of ${\mathcal{B}}_{\mathfrak{q}}$ by ${\mathfrak Z}_{\mathfrak{q}}$ where ${\mathfrak Z}_{\mathfrak{q}}$ is isomorphic to the …