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By a (finite) 2-group $X$, I mean a finite group $G$, a finite abelian group $A$, an action of $G$ on $\operatorname{Aut}(A)$, as well as a 3-cocycle $\alpha\in H^3(BG, A)$. They are also equivalent t …

I'm trying to understand CFT from a purely axiomatic-field-theoretical perspective. That is, there is a vector space $V$ associated to the circle, and an element of $V^{\otimes n}$ associated to every …

Added later: As Viktor Ostrik points out in a comment, what I'm looking for is a classification of so-called crossed $G$-algebras corresponding to homotopy TQFTs with homotopy target space $K(G, 1)$ a …

What is the original reference where it was first proven that the generators and relations of the 2-dimensional cobordism category are those of commutative Frobenius algebras? I've seen this article b …

According to a definition by Segal, a $2$-dimensional CFT is a symmetric monoidal functor from the category of oriented conformal cobordisms to the cateogry of projective complex vectorspaces. Coming …

Are there any examples of finite-dimensional complex non-semisimple non-commutative symmetric Frobenius algebras? Or can one show that none exist? I went through this list of all complex associative a …

By "algebraic structure" I mean a finite set of linear operators between tensor products of copies of one (or more) finite-dimensional (complex or real) vector spaces, fulfilling a set of axioms with …

Is there a general classification of special symmetric Frobenius algebras over real vector spaces? I know that $n\times n$ matrix algebras, the quaternions, the complex numbers, the trivial algebra, a …

It is very well known in the field of TQFT that the 2-dimensional oriented cobordism category is generated by the disk and the pair of pants (each going in both directions), subject to a finite set of …

(Fractional) quantum Hall systems are $2+1$-dimensional models which are said to possess topological order. One (maybe even complete) set of invariants of topological phases in $2+1$ dimensions is giv …

By having a time-reversal symmetry I mean that there is a local anti-unitary symmetry (representing the non-trivial element of $Z_2$) of the state-sum construction (or, if you want, of the associated …

This is a very basic beginners question about Chern-Simons theory. The configurations that we sum over to get the partition function are given by a Lie-algebra valued 1-form $A$ on a topological 3-man …

I often read that fully extended TQFTs are supposed to classify topological phases of matter. So I would like to understand the formal nature of fully extended TQFTs on a more direct physical level (w …

In Chern-Simons theory, one has modular fusion categories that are labelled by a Lie algebra and a "level", e.g. $SU(2)_2$ ("$SU(2)$ level $2$"). Physically this modular fusion category describes the …

I'd like to bring together the following two notions of "non-chiral": On the abstract algebraic side, a modular fusion category describing the anyon content of some physical system is said to be non- …