References
- Ai, C., Dong, C., Jiao, X., Ren, L. (2018). The irreducible modules and fusion rules for the parafermion vertex operator algebras. Trans. Amer. Math. Soc. 370(8):5963–5981. DOI: https://doi.org/10.1090/tran/7302.
- Borcherds, R. E. (1986). Vertex algebras, Kac-Moody algebras, and the Monster. Proc. Natl. Acad. Sci. USA 83(10):3068–3071. DOI: https://doi.org/10.1073/pnas.83.10.3068.
- Carnahan, S., Miyamoto, M. (2016). Regularity of fixed-point vertex operator subalgebras. arXiv: 1603.16045v4.
- Dong, C., Jiang, C. (2013). Representations of the vertex operator algebra VL2A4. J. Algebra 377:76–96. DOI: https://doi.org/10.1016/j.jalgebra.2012.12.004.
- Dong, C., Jiang, C., Jiang, Q., Jiao, X., Yu, N. (2015). Fusion rules for the vertex operator algebra VL2A4. J. Algebra 423:476–505. DOI: https://doi.org/10.1016/j.jalgebra.2014.10.027.
- Dong, C., Jiao, X., Xu, F. (2013). Quantum dimensions and quantum Galois theory. Trans. Amer. Math. Soc. 365(12):6441–6469. DOI: https://doi.org/10.1090/S0002-9947-2013-05863-1.
- Dong, C., Lam, C., Yamada, H. (2009). W-algebras related to parafermion vertex operator algebras. J. Algebra 322(7):2366–2403. DOI: https://doi.org/10.1016/j.jalgebra.2009.03.034.
- Dong, C., Li, H., Mason, G. (1996). Compact automorphism groups of vertex operator algebras. Internat. Math. Res. Notices 1996(18):913–921. DOI: https://doi.org/10.1155/S1073792896000566.
- Dong, C., Li, H., Mason, G. (1996). Simple currents and extensions of vertex operator algebras. Communmath. Phys. 180(3):671–707. DOI: https://doi.org/10.1007/BF02099628.
- Dong, C., Li, H., Mason, G. (1997). Regularity of rational vertex operator algebras. Adv. Math. 132(1):148–166. DOI: https://doi.org/10.1006/aima.1997.1681.
- Dong, C., Li, H., Mason, G. (1998). Twisted representations of vertex operator algebras. Math. Ann. 310(3):571–600. DOI: https://doi.org/10.1007/s002080050161.
- Dong, C., Li, H., Mason, G. (2000). Modular invariance of trace functions in orbifold theory and generalized moonshine. Comm. Math. Phys. 214(1):1–56. DOI: https://doi.org/10.1007/s002200000242.
- Dong, C., Mason, G. (1997). On quantum Galois theory. Duke Math. J. 86(2):305–321. DOI: https://doi.org/10.1215/S0012-7094-97-08609-9.
- Dong, C., Nagatomo, K. (1999). Representations of vertex operator algebra VL+ for rank one lattice L. Comm. Math. Phys. 202(1):169–195. DOI: https://doi.org/10.1007/s002200050578.
- Dong, C., Ren, L., Xu, F. (2017). On orbifold theory. Adv. Math. 321:1–30. DOI: https://doi.org/10.1016/j.aim.2017.09.032.
- Dong, C., Wang, Q. (2016). Quantum dimensions and fusion rules for parafermion vertex operator algebras. Proc. Amer. Math. Soc. 144(4):1483–1492. DOI: https://doi.org/10.1090/proc/12838.
- Dong, C., Yamskulna, G. (2002). Vertex operator algebras, generalized double and dual pairs. Math. Z. 241(2):397–423. DOI: https://doi.org/10.1007/s002090200421.
- Frenkel, I. B., Huang, Y.-Z., Lepowsky, J. (1993). On axiomatic approaches to vertex operator algebras and modules. Memoirs of the AMS 104(494):79. DOI: https://doi.org/10.1090/memo/0494.
- Frenkel, I. B., Lepowsky, J., Meurman, A. (1988). Vertex Operator Algebras and the Monster. Pure Appl. Math. Vol. 134. Massachusetts: Academic Press.
- Frenkel, I. B., Zhu, Y. (1992). Vertex operator algebras associated to representations of affine and Virasoro algebra. Duke Math. J. 66(1):123–168. DOI: https://doi.org/10.1215/S0012-7094-92-06604-X.
- Huang, Y.-Z. (1995). A theory of tensor products for module categories for a vertex operator algebra. IV. J. Pure Appl. Algebra 100(1–3):173–216. DOI: https://doi.org/10.1016/0022-4049(95)00050-7.
- Huang, Y.-Z., Lepowsky, J. (1995). A theory of tensor products for module categories for a vertex operator algebra. I, II. Selecta Mathematica, New. Series 1(4):699–756; 757–786. DOI: https://doi.org/10.1007/BF01587909.
- Huang, Y.-Z., Lepowsky, J. (1995). A theory of tensor products for module categories for a vertex operator algebra. III. J. Pure Appl. Algebra 100(1–3):141–171. DOI: https://doi.org/10.1016/0022-4049(95)00049-3.
- Jiang, C., Wang, Q. (2019). Fusion rules for Z2-orbifolds of affine and parafermion vertex operator algebras. arXiv:1904.01798.
- Jiang, C., Wang, B. (2020). Representations of the orbifold VOAS Lsl2̂(k,0)K and the commutant VOAS CLsom̂(1,0)⊗3(Lsom̂(3,0)). Bull. Malays. Math. Sci. Soc. DOI: https://doi.org/10.1007/s40840-020-00958-z. arXiv:1909.08173v2.
- Jiang, C., Wang, Q. (2019). Representations of Z2-orbifold of the parafermion vertex operator algebra K(sl2,k). J. Algebra 529:174–195. DOI: https://doi.org/10.1016/j.jalgebra.2019.03.032.
- Lepowsky, J., Li, H. (2004). Introduction to Vertex Operator Algebras and Their Representations. Progress in Math. Vol. 227. Boston: Birkhäuser.
- Li, H. (1996). Local systems of twisted vertex operators, vertex operator superalgebras and twisted modules. Contemp. Math. 193:203–236.
- Li, H. (1997). The physics superselection principle in vertex operator algebra theory. J. Algebra 196(2):436–457. DOI: https://doi.org/10.1006/jabr.1997.7126.
- Miyamoto, M. (2015). C2-cofiniteness of cyclic-orbifold models. Commun. Math. Phys. 335(3):1279–1286. DOI: https://doi.org/10.1007/s00220-014-2252-1.
- Miyamoto, M., Tanabe, K. (2004). Uniform product of Ag,n(V) for an orbifold model V and G-twisted Zhu algebra. J. Algebra 274(1):80–96. DOI: https://doi.org/10.1016/j.jalgebra.2003.11.017.
- Tsuchiya, A., Kanie, Y. (1988). Vertex operators in conformal field theory on P1 and monodromy representations of braid group. Conformal Field Theory and Solvable Lattice Models, Adv. Studies in Pure Math. Vol. 16. New York: Academic Press, pp. 297–372.
- Wang, B. Representations and fusion rules for the orbifold vertex operator algebras Lsl2̂(k,0)Z3. arXiv:2001.04275.
- Xu, F. (2000). Algebraic orbifold conformal field theories. Proc. Natl. Acad. Sci. USA 97(26):14069–14073. DOI: https://doi.org/10.1073/pnas.260375597.
- Xu, X. (1998). Introduction to Vertex Operator Superalgebras and Their Modules, Mathematics and Its Applications. The Netherlands: Kluwer Academic Publishers.
- Zhu, Y. (1996). Modular invariance of characters of vertex operator algebras. J. Amer. Math. Soc. 9(1):237–302. DOI: https://doi.org/10.1090/S0894-0347-96-00182-8.