The Lyubashenko Modular Functor for Drinfeld Centers via Non-Semisimple String-Nets
arxiv(2023)
Abstract
The Levin-Wen string-nets of a spherical fusion category $\mathcal{C}$
describe, by results of Kirillov and Bartlett, the representations of mapping
class groups of closed surfaces obtained from the Turaev-Viro construction
applied to $\mathcal{C}$. We provide a far-reaching generalization of this
statement to arbitrary pivotal finite tensor categories, including
non-semisimple or non-spherical ones: We show that the finitely cocompleted
string-net modular functor built from the projective objects of a pivotal
finite tensor category is equivalent to Lyubashenko's modular functor built
from the Drinfeld center $Z(\mathcal{C})$.
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