Araştırma Makalesi
BibTex RIS Kaynak Göster

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

Yıl 2021, Cilt: 29 Sayı: 29, 223 - 238, 05.01.2021
https://doi.org/10.24330/ieja.852237

Öz

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.

Kaynakça

  • 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.
Yıl 2021, Cilt: 29 Sayı: 29, 223 - 238, 05.01.2021
https://doi.org/10.24330/ieja.852237

Öz

Kaynakça

  • 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.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Deepak Naıdu Bu kişi benim

Yayımlanma Tarihi 5 Ocak 2021
Yayımlandığı Sayı Yıl 2021 Cilt: 29 Sayı: 29

Kaynak Göster

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. Ocak 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, sy. 29 (Ocak 2021): 223-38. https://doi.org/10.24330/ieja.852237.
EndNote Naıdu D (01 Ocak 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, c. 29, sy. 29, ss. 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 (Ocak 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, c. 29, sy. 29, 2021, ss. 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.