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A simple sufficient condition for triviality of obstructions in the orbifold construction for subfactors

Toshihiko Masuda

Abstract


We present a simple sufficient condition for triviality of obstructions in the orbifold construction. As an application, we can show the existence of subfactors with principal graph $D_{2n}$ without full use of Ocneanu's paragroup theory.


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References


Böckenhauer, J. and Evans, D. E., Modular invariants, graphs and α-induction for nets of subfactors. I, Comm. Math. Phys. 197 (1998), no. 2, 361–386. https://doi.org/10.1007/s002200050455

Böckenhauer, J. and Evans, D. E., Modular invariants, graphs and α-induction for nets of subfactors. II, Comm. Math. Phys. 200 (1999), no. 1, 57–103. https://doi.org/10.1007/s002200050523

Böckenhauer, J. and Evans, D. E., Modular invariants, graphs and α-induction for nets of subfactors. III, Comm. Math. Phys. 205 (1999), no. 1, 183–228. https://doi.org/10.1007/s002200050673

Böckenhauer, J., Evans, D. E., and Kawahigashi, Y., On α-induction, chiral generators and modular invariants for subfactors, Comm. Math. Phys. 208 (1999), no. 2, 429–487. https://doi.org/10.1007/s002200050765

Evans, D. E. and Gannon, T., Near-group fusion categories and their doubles, Adv. Math. 255 (2014), 586–640. https://doi.org/10.1016/j.aim.2013.12.014

Evans, D. E. and Kawahigashi, Y., Orbifold subfactors from Hecke algebras, Comm. Math. Phys. 165 (1994), no. 3, 445–484.

Evans, D. E. and Kawahigashi, Y., Quantum symmetries on operator algebras, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1998, Oxford Science Publications.

Goodman, F. M. and Wenzl, H., Littlewood-Richardson coefficients for Hecke algebras at roots of unity, Adv. Math. 82 (1990), no. 2, 244–265. https://doi.org/10.1016/0001-8708(90)90090-A

Goto, S., Orbifold construction for non-AFD subfactors, Internat. J. Math. 5 (1994), no. 5, 725–746. https://doi.org/10.1142/S0129167X9400036X

Goto, S., Symmetric flat connections, triviality of Loi's invariant and orbifold subfactors, Publ. Res. Inst. Math. Sci. 31 (1995), no. 4, 609–624. https://doi.org/10.2977/prims/1195163917

Izumi, M., Application of fusion rules to classification of subfactors, Publ. Res. Inst. Math. Sci. 27 (1991), no. 6, 953–994. https://doi.org/10.2977/prims/1195169007

Izumi, M., Subalgebras of infinite $C^*$-algebras with finite Watatani indices. I. Cuntz algebras, Comm. Math. Phys. 155 (1993), no. 1, 157–182.

Izumi, M., Subalgebras of infinite $C^*$-algebras with finite Watatani indices. II. Cuntz-Krieger algebras, Duke Math. J. 91 (1998), no. 3, 409–461. https://doi.org/10.1215/S0012-7094-98-09118-9

Izumi, M., The structure of sectors associated with Longo-Rehren inclusions. I. General theory, Comm. Math. Phys. 213 (2000), no. 1, 127–179. https://doi.org/10.1007/s002200000234

Jones, V. F. R., Index for subfactors, Invent. Math. 72 (1983), no. 1, 1–25. https://doi.org/10.1007/BF01389127

Kawahigashi, Y., On flatness of Ocneanu's connections on the Dynkin diagrams and classification of subfactors, J. Funct. Anal. 127 (1995), no. 1, 63–107. https://doi.org/10.1006/jfan.1995.1003

Kawahigashi, Y., Classification of approximately inner automorphisms of subfactors, Math. Ann. 308 (1997), no. 3, 425–438. https://doi.org/10.1007/s002080050083

Loi, P. H., On automorphisms of subfactors, J. Funct. Anal. 141 (1996), no. 2, 275–293. https://doi.org/10.1006/jfan.1996.0128

Masuda, T., Extension of automorphisms of a subfactor to the symmetric enveloping algebra, Internat. J. Math. 12 (2001), no. 6, 637–659. https://doi.org/10.1142/S0129167X01000988

Wenzl, H., Hecke algebras of type $A_n$ and subfactors, Invent. Math. 92 (1988), no. 2, 349–383. https://doi.org/10.1007/BF01404457

Xu, F., Orbifold construction in subfactors, Comm. Math. Phys. 166 (1994), no. 2, 237–253.

Xu, F., The flat part of non-flat orbifolds, Pacific J. Math. 172 (1996), no. 1, 299–306.

Xu, F., New braided endomorphisms from conformal inclusions, Comm. Math. Phys. 192 (1998), no. 2, 349–403. https://doi.org/10.1007/s002200050302




DOI: http://dx.doi.org/10.7146/math.scand.a-26240

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