2000 character limit reached
Center construction for group-crossed tensor categories
Published 15 Apr 2024 in math.QA and math.CT | (2404.09972v2)
Abstract: We define the notion of the $(G,\Gamma)$-crossed center of a $(G,\Gamma)$-crossed tensor category in the sense of Natale. We show that the $(G, \Gamma)$-crossed center is a $(G \bowtie \Gamma, G \times \Gamma)$-braided tensor category. This construction generalizes the graded center construction for graded tensor categories and the equivariant center construction for tensor categories with group actions.
- Group actions on 2-categories. Manuscripta Math., 159(1-2):81–115, 2019.
- Tensor categories, volume 205 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 2015.
- César Galindo. Coherence for monoidal G𝐺Gitalic_G-categories and braided G𝐺Gitalic_G-crossed categories. J. Algebra, 487:118–137, 2017.
- Centers of graded fusion categories. Algebra Number Theory, 3(8):959–990, 2009.
- Nick Gurski. Coherence in three-dimensional category theory, volume 201 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 2013.
- Christian Kassel. Quantum groups, volume 155 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995.
- Tom Leinster. Higher operads, higher categories, volume 298 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2004.
- Shahn Majid. Representations, duals and quantum doubles of monoidal categories. In Proceedings of the Winter School on Geometry and Physics (Srní, 1990), number 26, pages 197–206, 1991.
- Sonia Natale. Crossed actions of matched pairs of groups on tensor categories. Tohoku Math. J. (2), 68(3):377–405, 2016.
- Mizuki Oikawa. Frobenius algebras associated with the α𝛼\alphaitalic_α-induction for equivariantly braided tensor categories. Ann. Henri Poincaré, 2024.
- Raza Sohail Sheikh. Group-crossed extensions of representation categories in algebraic quantum field theory. PhD thesis, Radboud University, Nijmegen, 2019.
- Vladimir Turaev. Homotopy field theory in dimension 3 and crossed group-categories. arXiv preprint math/0005291, 2000.
- On the graded center of graded categories. J. Pure Appl. Algebra, 217(10):1895–1941, 2013.
- Guido Zappa. Sulla costruzione dei gruppi prodotto di due dati sottogruppi permutabili tra loro. In Atti Secondo Congresso Un. Mat. Ital., Bologna, 1940, pages 119–125. Ed. Cremonese, Rome, 1942.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.