Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2018, Cilt: 5 Sayı: 2, 51 - 63, 29.05.2018

Gurmail Singh

https://doi.org/10.13069/jacodesmath.369865
Cited By: 1

Öz

Kaynakça

  • [1] Z. Arad, E. Fisman, M. Muzychuk, Generalized table algebras, Israel J. Math. 114(1) (1999) 29–60.
  • [2] H. I. Blau, Table algebras, European J. Combin. 30(6) (2009) 1426–1455.
  • [3] M. Cuntz, Integral modular data and congruences, J. Algebraic Combin. 29(3) (2009) 357–387.
  • [4] P. Francesco, P. Mathieu, D. Sénéchal, Conformal Field Theory, Springer–Verlag, New York, 1997.
  • [5] T. Gannon, Modular data: The algebraic combinatorics of conformal field theory, J. Algebraic Combin. 22(2) (2005) 211–250.
  • [6] A. Hanaki, I. Miyamoto, Classification of association schemes with small vertices, 2017, available at: math.shinshu-u.ac.jp/ hanaki/as/.
  • [7] D. G. Higman, Coherent algebras, Linear Algebra Appl. 93 (1987) 209–239.
  • [8] J. D. Qualls, Lectures on Conformal Field Theory, arXiv:1511.04074 [hep-th].
  • [9] E. L. Rees, Graphical Discussion of the Roots of a Quartic Equation, Amer. Math. Monthly 29(2) (1922) 51–55.
  • [10] M. Schottenloher, A Mathematical Introduction to Conformal Field Theory, Springer–Verlag, Berlin, Heidelberg, 2nd edition, 2008.
  • [11] G. Singh, Classification of homogeneous Fourier matrices, arXiv:1610.05353 [math.RA].
  • [12] B. Xu, Characters of table algebras and applications to association schemes, J. Combin. Theory Ser. A 115(8) (2008) 1358–1373.
  • [13] A. Zahabi, Applications of Conformal Field Theory and String Theory in Statistical Systems, Ph.D. dissertation, University of Helsinki, Helsinki, Finland, 2013.

Fourier matrices of small rank

Yıl 2018, Cilt: 5 Sayı: 2, 51 - 63, 29.05.2018

Gurmail Singh

https://doi.org/10.13069/jacodesmath.369865
Cited By: 1

Öz

Modular data is an important topic of study in rational conformal field theory.
Cuntz, using a computer, classified the Fourier matrices associated to modular data with rational entries up to rank $12$, see [3].
Here we use the properties of $C$-algebras arising from Fourier matrices to classify complex Fourier matrices under certain conditions up to rank $5$. Also, we establish some results that are helpful in recognizing $C$-algebras that not arising from Fourier matrices by just looking at the first row of their character tables.

Anahtar Kelimeler

Fourier matrices Modular data Fusion rings C-algebras

Kaynakça

  • [1] Z. Arad, E. Fisman, M. Muzychuk, Generalized table algebras, Israel J. Math. 114(1) (1999) 29–60.
  • [2] H. I. Blau, Table algebras, European J. Combin. 30(6) (2009) 1426–1455.
  • [3] M. Cuntz, Integral modular data and congruences, J. Algebraic Combin. 29(3) (2009) 357–387.
  • [4] P. Francesco, P. Mathieu, D. Sénéchal, Conformal Field Theory, Springer–Verlag, New York, 1997.
  • [5] T. Gannon, Modular data: The algebraic combinatorics of conformal field theory, J. Algebraic Combin. 22(2) (2005) 211–250.
  • [6] A. Hanaki, I. Miyamoto, Classification of association schemes with small vertices, 2017, available at: math.shinshu-u.ac.jp/ hanaki/as/.
  • [7] D. G. Higman, Coherent algebras, Linear Algebra Appl. 93 (1987) 209–239.
  • [8] J. D. Qualls, Lectures on Conformal Field Theory, arXiv:1511.04074 [hep-th].
  • [9] E. L. Rees, Graphical Discussion of the Roots of a Quartic Equation, Amer. Math. Monthly 29(2) (1922) 51–55.
  • [10] M. Schottenloher, A Mathematical Introduction to Conformal Field Theory, Springer–Verlag, Berlin, Heidelberg, 2nd edition, 2008.
  • [11] G. Singh, Classification of homogeneous Fourier matrices, arXiv:1610.05353 [math.RA].
  • [12] B. Xu, Characters of table algebras and applications to association schemes, J. Combin. Theory Ser. A 115(8) (2008) 1358–1373.
  • [13] A. Zahabi, Applications of Conformal Field Theory and String Theory in Statistical Systems, Ph.D. dissertation, University of Helsinki, Helsinki, Finland, 2013.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Gurmail Singh Bu kişi benim 0000-0002-0819-8221

Yayımlanma Tarihi 29 Mayıs 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 5 Sayı: 2

Kaynak Göster

APA Singh, G. (2018). Fourier matrices of small rank. Journal of Algebra Combinatorics Discrete Structures and Applications, 5(2), 51-63. https://doi.org/10.13069/jacodesmath.369865
AMA Singh G. Fourier matrices of small rank. Journal of Algebra Combinatorics Discrete Structures and Applications. Mayıs 2018;5(2):51-63. doi:10.13069/jacodesmath.369865
Chicago Singh, Gurmail. “Fourier matrices of small rank”. Journal of Algebra Combinatorics Discrete Structures and Applications 5, sy. 2 (Mayıs 2018): 51-63. https://doi.org/10.13069/jacodesmath.369865.
EndNote Singh G (01 Mayıs 2018) Fourier matrices of small rank. Journal of Algebra Combinatorics Discrete Structures and Applications 5 2 51–63.
IEEE G. Singh, “Fourier matrices of small rank”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 5, sy. 2, ss. 51–63, 2018, doi: 10.13069/jacodesmath.369865.
ISNAD Singh, Gurmail. “Fourier matrices of small rank”. Journal of Algebra Combinatorics Discrete Structures and Applications 5/2 (Mayıs2018), 51-63. https://doi.org/10.13069/jacodesmath.369865.
JAMA Singh G. Fourier matrices of small rank. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5:51–63.
MLA Singh, Gurmail. “Fourier matrices of small rank”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 5, sy. 2, 2018, ss. 51-63, doi:10.13069/jacodesmath.369865.
Vancouver Singh G. Fourier matrices of small rank. Journal of Algebra Combinatorics Discrete Structures and Applications. 2018;5(2):51-63.

Cited By

Diagonal torsion matrices associated with modular data
Algebra and Discrete Mathematics
https://doi.org/10.12958/adm1368