English

Uniqueness of unitary structure for unitarizable fusion categories

Quantum Algebra 2023-01-13 v2 Category Theory

Abstract

We show that every unitarizable fusion category, and more generally every semisimple C*-tensor category, admits a unique unitary structure. Our proof is based on a categorified polar decomposition theorem for monoidal equivalences between such categories. We prove analogous results for unitarizable braided fusion categories and module categories.

Keywords

Cite

@article{arxiv.1906.09710,
  title  = {Uniqueness of unitary structure for unitarizable fusion categories},
  author = {David Reutter},
  journal= {arXiv preprint arXiv:1906.09710},
  year   = {2023}
}

Comments

14 pages; v2: generalized main theorem to semisimple C*-tensor categories with possibly infinitely many simple objects