Morita classes of algebras in modular tensor categories
Category Theory
2009-02-24 v2 High Energy Physics - Theory
Quantum Algebra
Abstract
We consider algebras in a modular tensor category C. If the trace pairing of an algebra A in C is non-degenerate we associate to A a commutative algebra Z(A), called the full centre, in a doubled version of the category C. We prove that two simple algebras with non-degenerate trace pairing are Morita-equivalent if and only if their full centres are isomorphic as algebras. This result has an interesting interpretation in two-dimensional rational conformal field theory; it implies that there cannot be several incompatible sets of boundary conditions for a given bulk theory.
Cite
@article{arxiv.0708.1897,
title = {Morita classes of algebras in modular tensor categories},
author = {Liang Kong and Ingo Runkel},
journal= {arXiv preprint arXiv:0708.1897},
year = {2009}
}
Comments
28 pages, several figures, version to appear in Adv. Math