Morita equivalence of certain crossed products | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 6، دوره 19، شماره 1، آبان 2023، صفحه 103-125 اصل مقاله (563.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.48308/cgasa.19.1.103 | ||
| نویسنده | ||
| Adriana Mejia Castaño* | ||
| Departament of Matemathics and statistics, Universidad del Norte, Colombia | ||
| چکیده | ||
| We introduce an alternative criterion for Morita equivalence over graded tensor categories using equivariant centers and equivariantizations. While Morita equivalence has been extensively studied in the context of fusion categories, primarily through the examination of their centers, recent advancements have broadened its scope to encompass graded tensor categories. This paper presents a novel criterion for characterizing Morita equivalence in graded tensor categories by leveraging equivariant centers and equivariantizations. Notably, the identification of Morita equivalence can be expedited when the Brauer Picard groups are known, offering an efficient approach to establishing the equivalence relationship. To generalize the properties of fusion categories to finite tensor categories, we utilize theconcept of an exact module category, which was introduced by Etingof and Ostrik. Exact module categories offer an intermediary restriction between the semisimplemodule categories of a fusion category and more general cases that may not be semisimpleor finite. | ||
| کلیدواژهها | ||
| Morita equivalence؛ dual category؛ tensor category | ||
| مراجع | ||
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[1] Andruskiewitsch, N. and Mombelli, M., On module categories over finite-dimensional Hopf algebras, J. Algebra 314 (2007), 383-418.
[2] Etingof, P., Gelaki, S., Nikshych, D., and Ostrik, V., ``Tensor Categories'', AMS Mathematical Surveys and Monographs 205, 2015.
[3] Etingof, P., Nikshych, D., and Ostrik, V., Fusion Categories and homotopy theory, Quantum Topol. 1(3) (2010), 209-273.
[4] Etingof, P., Nikshych, D., and Ostrik, V., Weakly group-theoretical and solvable fusion categories, Adv. Math. 226 (2011), 176-205.
[5] Etingof, P. and Ostrik, V., Finite tensor categories, Mosc. Math. J. 4(3) (2004), 627-654. [6] Galindo, C., Clifford theory for tensor categories, J. Lond. Math. Soc. 83(2) (2011), 57-78. [7] Galindo, C., Jaklitsch, D., and Schweigert, C., Equivariant Morita theory for graded tensor categories, Bull. Belg. Math. Soc. Simon Stevin 29(2) (2022), 145-171.
[8] Gelaki, S., Naidu, D., and Nikshych, D., Centers of graded fusion categories, Algebra and Number Theory 3(8) (2009), 959-990.
[9] Galindo, C. and Plavnik, J., Tensor functors between Morita duals of fusion categories, Lett. Math. Phys. 107 (2017), 553–590.
[10] Greenough, J., ``Bimodule Categories and Monoidal 2-Structure'', Ph.D. Thesis, University of New Hampshire, 2010.
[11] Kirillov Jr, A., Modular categories and orbifold models II, arXiv:0110221 [math.QA].
[12] Majid, S., Representations, duals and quantum doubles of monoidal categories, Rend. Circ. Mat. Palermo Suppl. 26(2) (1991), 197-206.
[13] Mejia Castaño, A. and Mombelli, M., Crossed extensions of the corepresentation category of finite supergroup algebras. Int. J. math (2015), \url{https://doi.org/10.1142/S0129167X15500676}.
[14] Müger, M., Galois extensions of braided tensor categories and braided crossed G-categories, J. Algebra 277(1) (2004), 256-281.
[15] Nikshych, D., Non group-theoretical semisimple Hopf algebras from group actions on fusion categories, Sel. math., New ser. (2008), 145-161.
[16] Schauenburg, P., The monoidal center construction and bimodules, J. Pure Appl. Algebra 158 (2001), 325-346.
[17] Tambara, D., Invariants and semi-direct products for finite group actions on tensor categories, J. Math. Soc. Japan 53(2) (2001), 429–456. | ||
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