On the classification of the Grothendieck rings of non-self-dual modular categories Academic Article

abstract

• We develop a symbolic computational approach to classifying low-rank modular fusion categories, up to finite ambiguity. By a generalized form of Ocneanu rigidity due to Etingof, Ostrik and Nikshych, it is enough to classify modular fusion algebras of a given rank-that is, to determine the possible Grothendieck rings with modular realizations. We use this technique to classify modular categories of rank at most 5 that are non-self-dual, i.e. those for which some object is not isomorphic to its dual object. 2009 Elsevier Inc.

authors

• Rowell, Eric

published proceedings

• JOURNAL OF ALGEBRA

author list (cited authors)

• Hong, S., & Rowell, E.

citation count

• 7

complete list of authors

• Hong, Seung-moon||Rowell, Eric

publication date

• January 2010

publisher

• Elsevier  Publisher

published in

• Journal of Algebra  Journal

keywords

• Fusion Algebras
• Galois Groups
• Grobner Bases
• Modular Categories

Digital Object Identifier (DOI)

• 10.1016/j.jalgebra.2009.11.044

start page

• 1000

end page

• 1015

volume

• 324

issue

• 5

URL

• http://dx.doi.org/10.1016/j.jalgebra.2009.11.044