Questions tagged [nichols-algebras]

The Nichols algebra of a braided vector space is a braided Hopf algebra named after the mathematician Warren Nichols. It takes the role of quantum Borel part of a pointed Hopf algebra.

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Abstract characterization of certain Nichols algebra

Let $\mathcal{C}$ be a $k$-linear abelian monoidal category and $(V,c)$ a braided object in $\mathcal{C}$. This means that $c \in Aut(V \otimes V)$ and satisfies the Yang-Baxter equation. Let $\...
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If $H$ is a Hopf algebra, do we have $H^{cop}$ is a Hopf algebra?

Let $H=(H, m, u, \Delta, \epsilon, S)$ be a Hopf algebra, see for example the lecture notes, where $m$ is the multiplication, $u$ is the unit, $\Delta$ is the comultiplication, $\epsilon$ is the ...
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Quantum Serre relations and braided commutator.

I am reading the lecture notes. On page 21, it is said that when $a_{ij}=-1$, we have \begin{align} ad_c(x_i)^{1-a_{ij}}(x_j)=x_i^2x_j - (q+q^{-1})x_ix_jx_i+x_jx_i^2. \quad (1) \end{align} Here $ad_c(...