Pith. sign in

REVIEW 4 cited by

Centers of graded fusion categories

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 0905.3117 v1 pith:PKLMEEKM submitted 2009-05-19 math.QA

Shlomo Gelaki , Deepak Naidu , Dmitri Nikshych This is my paper
classification math.QA
keywords categoriesfusioncentercentersgradedmodularresulttambara-yamagami
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

Let C be a fusion category faithfully graded by a finite group G and let D be the trivial component of this grading. The center Z(C) of C is shown to be canonically equivalent to a G-equivariantization of the relative center Z_D(C). We use this result to obtain a criterion for C to be group-theoretical and apply it to Tambara-Yamagami fusion categories. We also find several new series of modular categories by analyzing the centers of Tambara-Yamagami categories. Finally, we prove a general result about existence of zeroes in S-matrices of weakly integral modular categories.

Discussion (0). Sign in to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. SymTFT Approach for Mixed States with Non-Invertible Symmetries

    quant-ph 2025-07 conditional novelty 7.0 of 10

    A SymTFT-based classification of 1+1d mixed-state phases with non-invertible strong and weak symmetries, with explicit lattice-model examples.

  2. Gauging Non-Invertible Symmetries in (2+1)d Topological Orders

    hep-th 2025-07 conditional novelty 7.0 of 10

    A framework for gauging non-invertible symmetries in (2+1)d TQFTs, unifying 0-form and 1-form gauging via surface algebras, with constraints and toric-code examples.

  3. Spontaneous breaking of non-invertible symmetries and duality to beyond-Landau transitions

    cond-mat.str-el 2026-05 unverdicted novelty 6.0 of 10

    Non-invertible symmetry-breaking phases are characterized by long-range order parameters obeying generalized algebra, with certain transitions dual to beyond-Landau points of invertible symmetries under precise condit...

  4. Non-invertible translation from Lieb-Schultz-Mattis anomaly

    cond-mat.str-el 2026-01 conditional novelty 6.0 of 10

    Gauging the full internal symmetry of a lattice system with an LSM anomaly turns lattice translation into a non-invertible operator whose fusion rules involve condensation defects.

Pith tools