Unitary Anchored Planar Algebras
Abstract
In our previous article (http://arxiv.org/abs/1607.06041), we established an equivalence between pointed pivotal module tensor categories and anchored planar algebras. This article introduces the notion of unitarity for both module tensor categories and anchored planar algebras, and establishes the unitary analog of the above equivalence. Our constructions use Baez's 2-Hilbert spaces (i.e., semisimple C∗-categories equipped with unitary traces), the unitary Yoneda embedding, and the notion of unitary adjunction for dagger functors between 2-Hilbert spaces.
- Publication:
-
Communications in Mathematical Physics
- Pub Date:
- June 2024
- DOI:
- 10.1007/s00220-024-04985-w
- arXiv:
- arXiv:2301.11114
- Bibcode:
- 2024CMaPh.405..137H
- Keywords:
-
- Mathematics - Quantum Algebra;
- Mathematics - Category Theory;
- 18M05;
- 18M30;
- 18M40;
- 18M65
- E-Print:
- 47 pages, updated to published version