73
Views
0
CrossRef citations to date
0
Altmetric
Articles

Real fusion rings with degrees 1 and 4

Pages 4320-4354 | Received 22 Aug 2016, Accepted 23 Apr 2020, Published online: 13 May 2020

References

  • Arad, Z., Blau, H. I. (1991). On table algebras and applications to finite group theory. J. Algebra 138:137–185. DOI: 10.1016/0021-8693(91)90195-E.
  • Arad, Z., Blau, H. I., Fisman, E., Muzychuk, M. Standard integral table algebras generated by elements of degree two. In preparation.
  • Arad, Z., Erez, Y., Muzychuk, M. (2006). On homogeneous standard integral table algebras of degree 4. Commun. Algebra 34(2):463–519. DOI: 10.1080/00927870500387572.
  • Arad, Z., Fisman, E., Miloslavsky, V., Muzychuk, M. (2000). On antisymmetric homogeneous integral table algebras of degree three. In Homogeneous Integral Table Algebras of Degree Three: A Trilogy. Volume 144 (684) of Mem. Amer. Math. Soc. Providence, RI: AMS, pp. 54–73. DOI: 10.1090/memo/0684.
  • Arad, Z., Xu, B., Chen, G., Cohen, E., Hussam, A., Muzychuk, M. (2011). On Normalized Integral Table Algebras (Fusion Rings). London: Springer.
  • Blau, H. I. (1997). Homogeneous integral table algebras of degree two. Algebra Colloq. 4(4):393–408.
  • Blau, H. I. (2000a). Integral table algebras and Bose-Mesner algebras with a faithful nonreal element of degree three. J. Algebra 231:484–545. DOI: 10.1006/jabr.1999.8188.
  • Blau, H. I. (2000b). Homogeneous integral table algebras of degree three with no nontrivial linear elements. In Homogeneous Integral Table Algebras of Degree Three: A Trilogy. Volume 144 (684) of Mem. Amer. Math. Soc. Providence, RI: AMS, pp. 74–89. DOI: 10.1090/memo/0684.
  • Blau, H. I. (2009). Table algebras. Eur. J. Combin. 30:1426–1455. DOI: 10.1016/j.ejc.2008.11.008.
  • Blau, H. I. (2013). Fusion rings with few degrees. J. Algebra 396:220–271. DOI: 10.1016/j.jalgebra.2013.07.029.
  • Blau, H. I., Chen, G. (2014). Table bases as unions of proper closed subsets. Algebr. Represent. Theor. 17:1527–1552. DOI: 10.1007/s10468-013-9458-3.
  • Blau, H. I., Xu, B., Kettlestrings, C. Class two nilpotent table algebras. In preparation.
  • Blau, H. I., Xu, B. (1998). On homogeneous integral table algebras. J. Algebra 199:142–168. DOI: 10.1006/jabr.1997.7192.
  • Blau, H. I., Xu, B. (2000). Homogeneous integral table algebras of degree three with a faithful real element. In Homogeneous Integral Table Algebras of Degree Three: A Trilogy. Volume 144 (684) of Mem. Amer. Math. Soc. Providence, RI: AMS, pp. 1–53. DOI: 10.1090/memo/0684.
  • Isaacs, I. M., Passman, D. S. (1965). A characterization of groups in terms of the degrees of their characters. Pacific J. Math. 15(3):877–903. DOI: 10.2140/pjm.1965.15.877.
  • Mitchell, T. L. (2015). Fusion rings with degrees 1 and 4. PhD thesis. DeKalb, IL: Northern Illinois University.
  • Passman, D. S. (1966). Groups whose irreducible representations have degrees dividing p2. Pacific J. Math. 17(3):475–496. DOI: 10.2140/pjm.1966.17.475.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.