2025/10/14 by Corey Jones, Jones, Corey, Emily McGovern +1
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2510.12675
openalex publication_date 2025/10/14 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
Discrete, unimodular inclusions of factors (N⊆ M, E) with N of type \rmII1 have a natural notion of standard invariant, generalizing the finite index case. When the unitary tensor category of N-N bimodules generated by NL2(M, τ∘ E)N is equivalent to the Temperley-Lieb-Jones category TLJ(δ), the associated discrete standard invariants are classified in terms of fair and balanced δ-graphs. Many examples of these subfactors naturally arise in the context of the Guionnet-Jones-Shlyakhtenko (GJS) construction for graphs. In this paper, we compute the discrete standard invariant of the centralizer subfactor N⊆ Mϕ for the canonical state ϕ=τ∘ E, which is again a discrete subfactor of TLJ(δ)-type. We show that the associated fair and balanced δ-graph behaves analogously to a universal covering space of the original fair and balanced δ-graph. As an application, we obtain an obstruction to the realization of discrete tracial TLJ-type standard invariants by subfactors of a \rmII1 factor M in terms of the fundamental group of M.