Ana Ros Camacho (Cardiff University, Wales), Yiby Morales (Universidad de Los Andes, Bogotá, Colombia))
If you wish to attend the talks, please contact Sylvie Paycha paycha@math.uni-potsdam.de for the login details.
14:00 Ana Ros Camacho (Cardiff University, Wales): A gentle introduction to fusion categories and algebra objects therein
15:30 Yiby Morales (Universidad de Los Andes, Bogotá, Colombia): Algebras in group-theoretical fusion categories
Abstracts:
Ana Ros Camacho (Cardiff University, Wales): A gentle introduction to fusion categories and algebra objects therein
In this talk we will introduce the notion of fusion categories. Roughly speaking these are categories finite in some sense, equipped with a tensor product and duals. We will also introduce the notion of algebra object in these categories, which mimics the usual notion of algebra but in a categorical setting, and explain some of the properties they can display. We will not assume familiarity with categories, and will include many examples for the sake of clarity.
Yiby Morales (Universidad de Los Andes, Bogotá, Colombia): Algebras in group-theoretical fusion categories
In this talk, we will discuss the concept of module category, and what it means for a module category to be represented by an algebra. This will lead us to the notion of Morita equivalence of algebras. We will also dive into some special kind of fusion categories, namely pointed fusion categories and group-theoretical fusion categories. Sonia Natale and Victor Ostrik described algebras representing the Morita equivalence classes in pointed fusion categories, and we will explain how this result can be generalized to group-theoretical fusion categories.
