MathOverflow

Let $A$ be an algebra and $H$ be a Hopf algebra. We say that $H$ is a Hopf symmetry of $A$ if $A$ is an $H$-module algebra, i.e., if $H$ has an action on $A$ that respects the multiplication and unit of $A$:\begin{eqnarray}h.(ab)&=&(h_{(1)}.a...

In the most responsive way, I address the mathematical community. I'm here asking for the community's support. This morning I visited arXiv and noticed that an article has been accepted on arXiv. It fabricates a narrative and attempts to claim my Equivalence...

Let $\mathcal{C}$ be a unitary fusion category, and let $Z(\mathcal{C})$ be its Drinfeld center. Suppose $Z(\mathcal{C})$ has a fiber functor $F: Z(\mathcal{C})\to \mathrm{Vec}$. Question: must $\mathcal{C}$ itself also have a fiber functor?

Let $\pi$ be a permutation of size $n$ and let $L(\pi)=[L_1,...,L_n]$ be the Lehmer code (https://en.wikipedia.org/wiki/Lehmer_code) of $\pi$, that is $L_i:=|\{j>i \mid \pi(j)<\pi(i) \}|$.
Associate to $\pi$ its Cartan matrix $A(\pi)$ defined by the $n \times n$-matrix with entries $a_{r,i}=1$ if $i \leq r \leq t_i$ with $t_i:=i+L_i \in \{i,...,n\}$ and zero entries else....