Research Article
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Year 2020, Volume 28, Issue 28, 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, Volume 28, Issue 28, 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.

Details

Primary Language English
Subjects Mathematics
Journal Section Articles
Authors

Deepak NAIDU This is me (Primary Author)
Northern Illinois University
United States

Publication Date July 14, 2020
Published in Issue 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 <https://dergipark.org.tr/en/pub/ieja/issue/55997/768210>
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