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SOME PROPERTIES OF THE REPRESENTATION CATEGORY OF TWISTED DRINFELD DOUBLES OF FINITE GROUPS

Year 2021, , 223 - 238, 05.01.2021
https://doi.org/10.24330/ieja.852237

Abstract

A criterion for a simple object of the representation category
$\Rep(D^\omega(G))$ of the twisted Drinfeld double $D^\omega(G)$
to be a generator is given, where $G$ is a finite group and $\omega$ is
a 3-cocycle on $G$. A description of the adjoint category of
$\Rep(D^\omega(G))$ is also given.

References

  • B. Bakalov and A. Kirillov Jr., Lectures on Tensor Categories and Modular Functors, University Lecture Series, 21, American Mathematical Society, Providence, RI, 2001.
  • A. Coste, T. Gannon and P. Ruelle, Finite group modular data, Nuclear Phys. B, 581(3) (2000), 679-717.
  • R. Dijkgraaf, V. Pasquier and P. Roche, Quasi-quantum groups related to orbifold models, Modern quantum field theory (Bombay, 1990), World Sci. Publ., River Edge, NJ, (1991), 375-383.
  • R. Dijkgraaf, V. Pasquier and P. Roche, Quasi-Hopf algebras, group cohomology, and orbifold models, Integrable systems and quantum groups (Pavia, 1990), World Sci. Publ., River Edge, NJ, (1992), 75-98.
  • L. Dornho, Group Representation Theory, Part A, M. Dekker (1971).
  • P. Etingof, D. Nikshych and V. Ostrik, On fusion categories, Ann. of Math. (2), 162 (2005), 581-642.
  • S. Gelaki and D. Nikshych, Nilpotent fusion categories, Adv. Math., 217 (2008), 1053-1071.
  • J. E. Humphreys, Representation of SL(2; p), Amer. Math. Monthly, 82 (1975), no. 1, 21-39.
  • H. Jordan, Group characters of various types of linear groups, Amer. J. Math., 29 (1907), 387-405.
  • M. Muger, On the structure of modular categories, Proc. London Math. Soc., 87(2) (2003), 291-308.
  • D. Naidu and D. Nikshych, Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groups, Comm. Math. Phys., 279 (2008), 845-872.
  • D. Naidu, D. Nikshych and S. Witherspoon, Fusion subcategories of representation categories of twisted quantum doubles of finite groups, Int. Math. Res. Not. IMRN, 22 (2009), 4183-4219.
  • I. Schur, Untersuchungen uber die Darstellungen der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math., 132 (1907) 85-137.
Year 2021, , 223 - 238, 05.01.2021
https://doi.org/10.24330/ieja.852237

Abstract

References

  • B. Bakalov and A. Kirillov Jr., Lectures on Tensor Categories and Modular Functors, University Lecture Series, 21, American Mathematical Society, Providence, RI, 2001.
  • A. Coste, T. Gannon and P. Ruelle, Finite group modular data, Nuclear Phys. B, 581(3) (2000), 679-717.
  • R. Dijkgraaf, V. Pasquier and P. Roche, Quasi-quantum groups related to orbifold models, Modern quantum field theory (Bombay, 1990), World Sci. Publ., River Edge, NJ, (1991), 375-383.
  • R. Dijkgraaf, V. Pasquier and P. Roche, Quasi-Hopf algebras, group cohomology, and orbifold models, Integrable systems and quantum groups (Pavia, 1990), World Sci. Publ., River Edge, NJ, (1992), 75-98.
  • L. Dornho, Group Representation Theory, Part A, M. Dekker (1971).
  • P. Etingof, D. Nikshych and V. Ostrik, On fusion categories, Ann. of Math. (2), 162 (2005), 581-642.
  • S. Gelaki and D. Nikshych, Nilpotent fusion categories, Adv. Math., 217 (2008), 1053-1071.
  • J. E. Humphreys, Representation of SL(2; p), Amer. Math. Monthly, 82 (1975), no. 1, 21-39.
  • H. Jordan, Group characters of various types of linear groups, Amer. J. Math., 29 (1907), 387-405.
  • M. Muger, On the structure of modular categories, Proc. London Math. Soc., 87(2) (2003), 291-308.
  • D. Naidu and D. Nikshych, Lagrangian subcategories and braided tensor equivalences of twisted quantum doubles of finite groups, Comm. Math. Phys., 279 (2008), 845-872.
  • D. Naidu, D. Nikshych and S. Witherspoon, Fusion subcategories of representation categories of twisted quantum doubles of finite groups, Int. Math. Res. Not. IMRN, 22 (2009), 4183-4219.
  • I. Schur, Untersuchungen uber die Darstellungen der endlichen Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math., 132 (1907) 85-137.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Deepak Naıdu This is me

Publication Date January 5, 2021
Published in Issue Year 2021

Cite

APA Naıdu, D. (2021). SOME PROPERTIES OF THE REPRESENTATION CATEGORY OF TWISTED DRINFELD DOUBLES OF FINITE GROUPS. International Electronic Journal of Algebra, 29(29), 223-238. https://doi.org/10.24330/ieja.852237
AMA Naıdu D. SOME PROPERTIES OF THE REPRESENTATION CATEGORY OF TWISTED DRINFELD DOUBLES OF FINITE GROUPS. IEJA. January 2021;29(29):223-238. doi:10.24330/ieja.852237
Chicago Naıdu, Deepak. “SOME PROPERTIES OF THE REPRESENTATION CATEGORY OF TWISTED DRINFELD DOUBLES OF FINITE GROUPS”. International Electronic Journal of Algebra 29, no. 29 (January 2021): 223-38. https://doi.org/10.24330/ieja.852237.
EndNote Naıdu D (January 1, 2021) SOME PROPERTIES OF THE REPRESENTATION CATEGORY OF TWISTED DRINFELD DOUBLES OF FINITE GROUPS. International Electronic Journal of Algebra 29 29 223–238.
IEEE D. Naıdu, “SOME PROPERTIES OF THE REPRESENTATION CATEGORY OF TWISTED DRINFELD DOUBLES OF FINITE GROUPS”, IEJA, vol. 29, no. 29, pp. 223–238, 2021, doi: 10.24330/ieja.852237.
ISNAD Naıdu, Deepak. “SOME PROPERTIES OF THE REPRESENTATION CATEGORY OF TWISTED DRINFELD DOUBLES OF FINITE GROUPS”. International Electronic Journal of Algebra 29/29 (January 2021), 223-238. https://doi.org/10.24330/ieja.852237.
JAMA Naıdu D. SOME PROPERTIES OF THE REPRESENTATION CATEGORY OF TWISTED DRINFELD DOUBLES OF FINITE GROUPS. IEJA. 2021;29:223–238.
MLA Naıdu, Deepak. “SOME PROPERTIES OF THE REPRESENTATION CATEGORY OF TWISTED DRINFELD DOUBLES OF FINITE GROUPS”. International Electronic Journal of Algebra, vol. 29, no. 29, 2021, pp. 223-38, doi:10.24330/ieja.852237.
Vancouver Naıdu D. SOME PROPERTIES OF THE REPRESENTATION CATEGORY OF TWISTED DRINFELD DOUBLES OF FINITE GROUPS. IEJA. 2021;29(29):223-38.