Title: Commutative algebra in braided tensor categories
Speaker: Alexei Davydov (Ohio University)
Abstract: Commutative separable algebras seem to play an important role in the emerging structure theory of finite braided tensor categories.
The construction of the category of local modules can be seen as the procedure of “contracting” a commutative algebra. These contractions reduce the dimension of the category and eventually produce a category without commutative algebras (a completely anisotropic category).
Deligne’s theorem implies that in characteristic zero there are only two completely anisotropic symmetric categories - the category of vector spaces Vect and its super analogue sVect. This has an implication for all braided fusion categories, grouping them into two classes - with symmetric centres contractible to either Vect or sVect. It happens that the completely anisotropic categories in each class form a group under the Deligne tensor product of categories. These are the Witt groups of non-degenerate and slightly degenerate braided fusion categories.
Seminar URL: http://yutsumura.com/quantum-algebra-topology-seminar/
