Classification of Pointed Fusion Categories of dimension 8 up to weak Morita equivalence

ABSTRACT

In this paper we give a complete classification of pointed fusion categories over ℂ of global dimension 8. We first classify the equivalence classes of pointed fusion categories of dimension 8, and then we proceed to determine which of these equivalence classes have equivalent categories of modules following the procedure presented in [9, 11]. The results of this paper permit to recover the classification of twisted quantum doubles of groups of order 8 up to gauge equivalence of braided quasi-Hopf algebras that was previously done in [6] and [5].

KEYWORDS:

• Pointed Fusion Category
• tensor category
• weak Morita equivalence

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 18D10
• Secondary 20J06