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EXAMPLES OF (NON-)BRAIDED TENSOR CATEGORIES

Year 2020, , 194 - 205, 07.01.2020
https://doi.org/10.24330/ieja.663066

Abstract

Six examples of non-braidable tensor categories which are extensions of the category $Comod(H)$, for $H$ a supergroup algebra; and two examples of braided categories where the only possible braiding is the trivial braiding are introduced.

References

  • N. Andruskiewitsch and M. Grana, Braided Hopf algebras over non abelian finite groups, Colloquium on Operator Algebras and Quantum Groups (Spanish) (Vaquerias, 1997), Bol. Acad. Nac. Cienc. (Cordoba), 63 (1999), 45-78.
  • P. Etingof and S. Gelaki, The classification of finite-dimensional triangular Hopf algebras over an algebraically closed field of characteristic 0, Mosc. Math. J., 3(1) (2003), 37-43.
  • C. Galindo, Crossed product tensor categories, J. Algebra, 337 (2011), 233-252.
  • T. J. Hagge and S.-M. Hong, Some non-braided fusion categories of rank three, Commun. Contemp. Math., 11(4) (2009), 615-637.
  • A. Joyal and R. Street, Braided Monoidal Categories, Macquarie Math. Reports, Report No: 860081, November 1986.
  • A. Masuoka, Cocycle deformations and Galois objects for some cosemisimple Hopf algebras of finite dimension, in New trends in Hopf algebra theory (La Falda, 1999), Contemp. Math., 267 (2000), 195-214.
  • A. Masuoka, Example of almost commutative Hopf algebras which are not coquasitriangular, Hopf algebras, Lecture Notes in Pure and Appl. Math., Dekker, New York, 237 (2004), 185-191.
  • A. Mejia Castano and M. Mombelli, Crossed extensions of the corepresentation category of finite supergroup algebras, Internat. J. Math., 26(9) (2015), 1550067 (26 pp).
  • S. Montgomery, Hopf Algebras and Their Actions on Rings, CBMS Regional Conference Series in Mathematics, 82, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the Amer. Math. Soc., Providence, RI, 1993.
  • P. Schauenburg, Hopf bi-Galois extensions, Comm. Algebra, 24(12) (1996), 3797-3825.
Year 2020, , 194 - 205, 07.01.2020
https://doi.org/10.24330/ieja.663066

Abstract

References

  • N. Andruskiewitsch and M. Grana, Braided Hopf algebras over non abelian finite groups, Colloquium on Operator Algebras and Quantum Groups (Spanish) (Vaquerias, 1997), Bol. Acad. Nac. Cienc. (Cordoba), 63 (1999), 45-78.
  • P. Etingof and S. Gelaki, The classification of finite-dimensional triangular Hopf algebras over an algebraically closed field of characteristic 0, Mosc. Math. J., 3(1) (2003), 37-43.
  • C. Galindo, Crossed product tensor categories, J. Algebra, 337 (2011), 233-252.
  • T. J. Hagge and S.-M. Hong, Some non-braided fusion categories of rank three, Commun. Contemp. Math., 11(4) (2009), 615-637.
  • A. Joyal and R. Street, Braided Monoidal Categories, Macquarie Math. Reports, Report No: 860081, November 1986.
  • A. Masuoka, Cocycle deformations and Galois objects for some cosemisimple Hopf algebras of finite dimension, in New trends in Hopf algebra theory (La Falda, 1999), Contemp. Math., 267 (2000), 195-214.
  • A. Masuoka, Example of almost commutative Hopf algebras which are not coquasitriangular, Hopf algebras, Lecture Notes in Pure and Appl. Math., Dekker, New York, 237 (2004), 185-191.
  • A. Mejia Castano and M. Mombelli, Crossed extensions of the corepresentation category of finite supergroup algebras, Internat. J. Math., 26(9) (2015), 1550067 (26 pp).
  • S. Montgomery, Hopf Algebras and Their Actions on Rings, CBMS Regional Conference Series in Mathematics, 82, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the Amer. Math. Soc., Providence, RI, 1993.
  • P. Schauenburg, Hopf bi-Galois extensions, Comm. Algebra, 24(12) (1996), 3797-3825.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Mejia Castano Adriana This is me

Publication Date January 7, 2020
Published in Issue Year 2020

Cite

APA Adriana, M. C. (2020). EXAMPLES OF (NON-)BRAIDED TENSOR CATEGORIES. International Electronic Journal of Algebra, 27(27), 194-205. https://doi.org/10.24330/ieja.663066
AMA Adriana MC. EXAMPLES OF (NON-)BRAIDED TENSOR CATEGORIES. IEJA. January 2020;27(27):194-205. doi:10.24330/ieja.663066
Chicago Adriana, Mejia Castano. “EXAMPLES OF (NON-)BRAIDED TENSOR CATEGORIES”. International Electronic Journal of Algebra 27, no. 27 (January 2020): 194-205. https://doi.org/10.24330/ieja.663066.
EndNote Adriana MC (January 1, 2020) EXAMPLES OF (NON-)BRAIDED TENSOR CATEGORIES. International Electronic Journal of Algebra 27 27 194–205.
IEEE M. C. Adriana, “EXAMPLES OF (NON-)BRAIDED TENSOR CATEGORIES”, IEJA, vol. 27, no. 27, pp. 194–205, 2020, doi: 10.24330/ieja.663066.
ISNAD Adriana, Mejia Castano. “EXAMPLES OF (NON-)BRAIDED TENSOR CATEGORIES”. International Electronic Journal of Algebra 27/27 (January 2020), 194-205. https://doi.org/10.24330/ieja.663066.
JAMA Adriana MC. EXAMPLES OF (NON-)BRAIDED TENSOR CATEGORIES. IEJA. 2020;27:194–205.
MLA Adriana, Mejia Castano. “EXAMPLES OF (NON-)BRAIDED TENSOR CATEGORIES”. International Electronic Journal of Algebra, vol. 27, no. 27, 2020, pp. 194-05, doi:10.24330/ieja.663066.
Vancouver Adriana MC. EXAMPLES OF (NON-)BRAIDED TENSOR CATEGORIES. IEJA. 2020;27(27):194-205.