8 papers
On the KAK Decomposition and Equivalence Classes
Dawei Ding, Yu Liu, Zi-Wen Liu
The KAK decomposition is a fundamental tool in Lie theory and quantum computing. Despite its widespread use, the mathematical foundations remain incomplete, particularly regarding…
-algebras in m-categories
Yu Leon Liu
We prove a connectivity bound for maps of -operads of the form , and as a consequence, give an in…
From bordisms of three-manifolds to domain walls between topological orders
Yu Leon Liu, Dalton A R Sakthivadivel
We study a correspondence between spin three-manifolds and bosonic abelian topological orders. Let be a spin three-manifold. We can define a -dimensional topological ord…
Braiding on complex oriented Soergel bimodules
Yu Leon Liu
In this note, we study U(n) Soergel bimodules in the context of stable homotopy theory. We define the -category of -valued U(n) Soergel bimodul…
Unital k-Restricted Infinity-Operads
Amartya Shekhar Dubey, Yu Leon Liu
We study unital -operads by their arity restrictions. Given , we develop a model for unital -restricted -operads, which are variants of -operad…
A braided monoidal -category of Soergel bimodules
Yu Leon Liu, Aaron Mazel-Gee, David Reutter +2
The Hecke algebras for all symmetric groups taken together form a braided monoidal category that controls all quantum link invariants of type A and, by extension, the standard cano…