Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQ-system completion is a 3-functor
100
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Q-systems are unita
rate research
Read More
For a finite-index $mathrm{II}_1$ subfactor $N subset M$, we prove the existence of a universal Hopf $ast$-algebra (or, a discrete quantum group in the analytic language) acting on $M$ in a trace-preserving fashion and fixing $N$ pointwise. We call this Hopf $ast$-algebra the quantum Galois group for the subfactor and compute it in some examples of interest, notably for arbitrary irreducible finite-index depth-two subfactors. Along the way, we prove the existence of universal acting Hopf algebras for more general structures (tensors in enriched categories), in the spirit of recent work by Agore, Gordienko and Vercruysse.
A unitary fusion category is called $mathbb{Z}/2mathbb{Z}$-quadratic if it has a $mathbb{Z}/2mathbb{Z}$ group of invertible objects and one other orbit of simple objects under the action of this group. We give a complete classification of $mathbb{Z}/2mathbb{Z}$-quadratic unitary fusion categories. The main tools for this classification are skein theory, a generalization of Ostriks results on formal codegrees to analyze the induction of the group elements to the center, and a computation similar to Larsons rank-finiteness bound for $mathbb{Z}/3mathbb{Z}$-near group pseudounitary fusion categories. This last computation is contained in an appendix coauthored with attendees from the 2014 AMS MRC on Mathematics of Quantum Phases of Matter and Quantum Information.
In this paper we present background results in enriched category theory and enriched model category theory necessary for developing model categories of enriched functors suitable for doing functor calculus.
There exists a canonical functor from the category of fibrant objects of a model category modulo cylinder homotopy to its homotopy category. We show that this functor is faithful under certain conditions, but not in general.
In the context of infinity categories, we rethink the notion of derived functor in terms of correspondences. This is especially convenient for the description of a passage from an adjoint pair (F,G) of functors to a derived adjoint pair (LF,RG). In particular, canonicity of this passage becomes obvious. 2nd version: added comparison to Delignes definition (SGA4) and a discussion of diagrams of derived functors. Introduction rewritten and references added. 3rd version: description of Kan extensions in terms of correspondences more detailed. 4th version: the final version accepted to HHA.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
