Research Article
Year 2020, Volume 28, Issue 28, 156 - 174, 14.07.2020

### 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, Volume 28, Issue 28, 156 - 174, 14.07.2020

### 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.

### Details

Primary Language English Mathematics Articles Deepak NAIDU This is me (Primary Author) Northern Illinois University United States July 14, 2020 Year 2020, Volume 28, Issue 28

### Cite

 Bibtex @research article { ieja768210, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {1710 Sokak, No:41, Batikent/Ankara}, publisher = {Abdullah HARMANCI}, year = {2020}, volume = {28}, number = {28}, pages = {156 - 174}, doi = {10.24330/ieja.768210}, title = {MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS}, key = {cite}, author = {Naıdu, Deepak} } APA Naıdu, D. (2020). MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS . International Electronic Journal of Algebra , 28 (28) , 156-174 . DOI: 10.24330/ieja.768210 MLA Naıdu, D. "MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS" . International Electronic Journal of Algebra 28 (2020 ): 156-174 Chicago Naıdu, D. "MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS". International Electronic Journal of Algebra 28 (2020 ): 156-174 RIS TY - JOUR T1 - MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS AU - DeepakNaıdu Y1 - 2020 PY - 2020 N1 - doi: 10.24330/ieja.768210 DO - 10.24330/ieja.768210 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 156 EP - 174 VL - 28 IS - 28 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.768210 UR - https://doi.org/10.24330/ieja.768210 Y2 - 2022 ER - EndNote %0 International Electronic Journal of Algebra MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS %A Deepak Naıdu %T MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS %D 2020 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 28 %N 28 %R doi: 10.24330/ieja.768210 %U 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 AMA Naıdu D. MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS. IEJA. 2020; 28(28): 156-174. Vancouver Naıdu D. MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS. International Electronic Journal of Algebra. 2020; 28(28): 156-174. IEEE D. Naıdu , "MODULAR GROUP IMAGES ARISING FROM DRINFELD DOUBLES OF DIHEDRAL GROUPS", International Electronic Journal of Algebra, vol. 28, no. 28, pp. 156-174, Jul. 2020, doi:10.24330/ieja.768210