title：reconstruction of tensor categories from their invariants
speaker：prof. huixiang chen
from： yangzhou university
time：4:30pm-5:30pm, 10 sept
abstract：in this paper, we study the tensor categories of finite rank over an algebraically closed field
$\mathbb f$. given a data $(r, a, \phi, a)$ with some conditions supposed on it, where $r$ is a $\mathbb{z}_ $-ring of rank $n$ over $\mathbb z$, $a$ is a finite dimensional $\mathbb f$-algebra with a full set of $n$ primitive orthogonal idempotents, $\phi$ is an algebra map from $a\otimes_{\mathbb f}a$ to an algebra $m(r, a, n)$ constructed by $a$ and $r$, and $a=\{a_{i,j,l}|1\< i,j,l\moreover, it is shown that the new krull schmidt and abelian tensor category constructed from the data $(r, a, \phi, a)$ is tensor equivalent to the original category $\mathcal c$.
$\mathbb f$. given a data $(r, a, \phi, a)$ with some conditions supposed on it, where $r$ is a $\mathbb{z}_ $-ring of rank $n$ over $\mathbb z$, $a$ is a finite dimensional $\mathbb f$-algebra with a full set of $n$ primitive orthogonal idempotents, $\phi$ is an algebra map from $a\otimes_{\mathbb f}a$ to an algebra $m(r, a, n)$ constructed by $a$ and $r$, and $a=\{a_{i,j,l}|1\< i,j,l\
