Relation between bicrossed products and crossed extensions of fusion categories

• Monique Müller ^[1] ; Héctor Martín Peña Pollastri ^[3] ; Julia Plavnik ^[2]
  1. [1] Universidade Federal de São João del-Rei

     Universidade Federal de São João del-Rei

     Brasil

     
  2. [2] Vrije Universiteit Brussel

     Vrije Universiteit Brussel

     Arrondissement Brussel-Hoofdstad, Bélgica

     
  3. [3] Indiana University, USA

  Mostrar afiliaciones +
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 281-294
• Idioma: inglés
• DOI: 10.33044/revuma.5338
• Enlaces
  • Texto completo
• Resumen

  • We show that all crossed extensions defined by Natale can be recovered as duals of bicrossed products of fusion categories. As an application, we prove that any exact factorization between a pointed fusion category vecG and a fusion category C can be realized as a bicrossed product between vecG and C .

• Referencias bibliográficas
  • T. Basak and S. Gelaki, Exact factorizations and extensions of finite tensor categories, J. Algebra 631 (2023), 46–71. DOI MR Zbl
  • A. Bruguières and S. Natale, Exact sequences of tensor categories, Int. Math. Res. Not. IMRN no. 24 (2011), 5644–5705. DOI MR Zbl
  • P. Etingof and S. Gelaki, Exact sequences of tensor categories with respect to a module category, Adv. Math. 308 (2017), 1187–1208. DOI ...
  • P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor categories, Math. Surveys Monogr. 205, American Mathematical Society, Providence,...
  • S. Gelaki, Exact factorizations and extensions of fusion categories, J. Algebra 480 (2017), 505–518. DOI MR Zbl
  • C. Kassel, Quantum groups, Graduate Texts in Mathematics 155, Springer, New York, 1995. DOI MR Zbl
  • A. Kitaev, Anyons in an exactly solved model and beyond, Ann. Physics 321 no. 1 (2006), 2–111. DOI MR Zbl
  • S. MacLane, Categories for the working mathematician, Graduate Texts in Mathematics 5, Springer, New York, 1971. MR Zbl
  • S. Majid, Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction, J. Algebra 130 no....
  • S. Majid, Foundations of quantum group theory, Cambridge University Press, Cambridge, 1995. DOI MR Zbl
  • G. Moore and N. Seiberg, Classical and quantum conformal field theory, Comm. Math. Phys. 123 no. 2 (1989), 177–254. MR Zbl Available at...
  • M. Müller, H. M. Peña Pollastri, and J. Plavnik, On bicrossed product of fusion categories and exact factorizations, [v1] 2024, [v2] 2025....
  • S. Natale, Crossed actions of matched pairs of groups on tensor categories, Tohoku Math. J. (2) 68 no. 3 (2016), 377–405. DOI MR Zbl
  • S. Natale, Extensions of tensor categories by finite group fusion categories, Math. Proc. Cambridge Philos. Soc. 170 no. 1 (2021), 161–189....
  • D. Nikshych, Morita equivalence methods in classification of fusion categories, in Hopf algebras and tensor categories, Contemp. Math. 585,...
  • S. Sanford, Fusion categories over non-algebraically closed fields, J. Algebra 663 (2025), 316–351. DOI MR Zbl
  • M. Takeuchi, Matched pairs of groups and bismash products of Hopf algebras, Comm. Algebra 9 no. 8 (1981), 841–882. DOI MR Zbl