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Year 2020, , 156 - 174, 14.07.2020
https://doi.org/10.24330/ieja.768210

Abstract

References

  • B. Bakalov and A. Kirillov, Jr., Lectures on Tensor Categories and Modular Functors, University Lecture Series, 21, Amer. Math. Soc., 2001.
  • H. Behr and J. Mennicke, A presentation of the groups PSL(2; p), Canadian J. Math., 20 (1968), 1432-1438.
  • J. L. Cardy, Operator content of two-dimensional conformally invariant theories, Nuclear Phys. B, 270(2) (1986), 186-204.
  • A. Coste and T. Gannon, Congruence subgroups and rational conformal field theory, preprint, arXiv:math/9909080 [math.QA], (1999).
  • A. Coste, T. Gannon and P. Ruelle, Finite group modular data, Nucl. Phys. B, 581(3) (2000), 679-717.
  • R. C. Gunning, Lectures on Modular Forms, Notes by Armand Brumer, Annals of Mathematics Studies, 48, Princeton University Press, Princeton, N.J., 1962.
  • D. L. McQuillan, Classification of normal congruence subgroups of the modular group, Amer. J. Math., 87(2) (1965), 285-296.
  • S.-H. Ng and P. Schauenburg, Congruence subgroups and generalized Frobenius-Schur indicators, Comm. Math. Phys., 300(1) (2010), 1-46.
  • Y. Sommerhauser and Y. Zhu, Hopf Algebras and Congruence Subgroups, Mem. Amer. Math. Soc., 219(1028), 2012.

MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS

Year 2020, , 156 - 174, 14.07.2020
https://doi.org/10.24330/ieja.768210

Abstract

We show that the image of the representation of the modular group $\SL(2, \Z)$ arising from the representation category $\Rep(D(G))$ of the Drinfeld double $D(G)$
is isomorphic to the group $\PSL(2, \Zn) \times S_3$, when $G$ is either the dihedral group of order $2n$ or the dihedral group of order $4n$ for some odd integer $n \geq 3$. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$

References

  • B. Bakalov and A. Kirillov, Jr., Lectures on Tensor Categories and Modular Functors, University Lecture Series, 21, Amer. Math. Soc., 2001.
  • H. Behr and J. Mennicke, A presentation of the groups PSL(2; p), Canadian J. Math., 20 (1968), 1432-1438.
  • J. L. Cardy, Operator content of two-dimensional conformally invariant theories, Nuclear Phys. B, 270(2) (1986), 186-204.
  • A. Coste and T. Gannon, Congruence subgroups and rational conformal field theory, preprint, arXiv:math/9909080 [math.QA], (1999).
  • A. Coste, T. Gannon and P. Ruelle, Finite group modular data, Nucl. Phys. B, 581(3) (2000), 679-717.
  • R. C. Gunning, Lectures on Modular Forms, Notes by Armand Brumer, Annals of Mathematics Studies, 48, Princeton University Press, Princeton, N.J., 1962.
  • D. L. McQuillan, Classification of normal congruence subgroups of the modular group, Amer. J. Math., 87(2) (1965), 285-296.
  • S.-H. Ng and P. Schauenburg, Congruence subgroups and generalized Frobenius-Schur indicators, Comm. Math. Phys., 300(1) (2010), 1-46.
  • Y. Sommerhauser and Y. Zhu, Hopf Algebras and Congruence Subgroups, Mem. Amer. Math. Soc., 219(1028), 2012.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Deepak Naıdu This is me

Publication Date July 14, 2020
Published in Issue Year 2020

Cite

APA Naıdu, D. (2020). MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS. International Electronic Journal of Algebra, 28(28), 156-174. https://doi.org/10.24330/ieja.768210
AMA Naıdu D. MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS. IEJA. July 2020;28(28):156-174. doi:10.24330/ieja.768210
Chicago Naıdu, Deepak. “MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS”. International Electronic Journal of Algebra 28, no. 28 (July 2020): 156-74. https://doi.org/10.24330/ieja.768210.
EndNote Naıdu D (July 1, 2020) MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS. International Electronic Journal of Algebra 28 28 156–174.
IEEE D. Naıdu, “MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS”, IEJA, vol. 28, no. 28, pp. 156–174, 2020, doi: 10.24330/ieja.768210.
ISNAD Naıdu, Deepak. “MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS”. International Electronic Journal of Algebra 28/28 (July 2020), 156-174. https://doi.org/10.24330/ieja.768210.
JAMA Naıdu D. MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS. IEJA. 2020;28:156–174.
MLA Naıdu, Deepak. “MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS”. International Electronic Journal of Algebra, vol. 28, no. 28, 2020, pp. 156-74, doi:10.24330/ieja.768210.
Vancouver Naıdu D. MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS. IEJA. 2020;28(28):156-74.