Invertible projective 2-representations from invertible 2d TQFTs with defects

2025/09/20 by Domenico Fiorenza, Fiorenza, Domenico, Chetan Vuppulury +1
Computer Science · Engineering · Mathematics · #57R56 #Category Theory (math.CT) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings, Modules, and Algebras #graph theory and CDMA systems #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2509.16626

openalex publication_date 2025/09/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

We investigate invertible projective representations and their 2-categorical analogues using the language of TQFTs with defects. The main result is a freeness property for invertible projective representatios. While trivial in the 1-categorical setting, this result becomes interesting for 2-representations: as an application, only relying only on invertibility of Clifford algebras and Fock bimodules in the Morita 2-category of super vector spaces we recover Ludewig--Roos' result that the Clifford/Fock construction is a projective 2-representation of the category of Lagrangian correspondences.

Citations

• Projective and anomalous representations of categories and their linearizations
• Three quick recipes with fully extended oriented 2d TQFTs
• The Chiral Anomaly of the Free Fermion in Functorial Field Theory
• Traces in symmetric monoidal categories
• Heisenberg algebra and a graphical calculus
• On the Classification of Topological Field Theories
• Topological quantum field theories

Related

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