27 citations · 71 across the 31 of their papers we have counts for
19 papers · 1 filter
Fully exact and fully dualizable module categories
Azat M. Gainutdinov, Robert Laugwitz
We define fully exact module categories, a subclass of exact module categories over a finite braided tensor category that is stable under the relative Deligne product. In contrast,…
Temperley-Lieb categories with coloured regions and Jones-Wenzl projectors
Cameron Howat, Robert Laugwitz, Martin Ray
Generalised Temperley-Lieb categories with regions labelled by elements of a commutative algebra were introduced by M. Khovanov and the second author in [Pure Appl. Math. Q. 19 (20…
Presentations for small reflection equation algebras of type A
Juliet Cooke, Robert Laugwitz
We give presentations, in terms of the generators and relations, for the reflection equation algebras of type and , i.e., the covariantized algebras of the dual Hopf a…
Frobenius monoidal functors induced by Frobenius extensions of Hopf algebras
Johannes Flake, Robert Laugwitz, Sebastian Posur
We show that induction along a Frobenius extension of Hopf algebras is a Frobenius monoidal functor in great generality, in particular, for all finite-dimensional and all pointed H…
Shifted Poisson structures on higher Chevalley-Eilenberg algebras
Cameron Kemp, Robert Laugwitz, Alexander Schenkel
This paper develops a graphical calculus to determine the -shifted Poisson structures on finitely generated semi-free commutative differential graded algebras. When applied to t…
Infinitesimal 2-braidings from 2-shifted Poisson structures
Cameron Kemp, Robert Laugwitz, Alexander Schenkel
It is shown that every -shifted Poisson structure on a finitely generated semi-free commutative differential graded algebra defines a very explicit infinitesimal -braidin…
Reflective centers of module categories and quantum K-matrices
Robert Laugwitz, Chelsea Walton, Milen Yakimov
Our work is motivated by obtaining solutions to the quantum reflection equation (qRE) by categorical methods. To start, given a braided monoidal category and $\mathca…
Frobenius Monoidal Functors of Dijkgraaf-Witten Categories and Rigid Frobenius Algebras
Samuel Hannah, Robert Laugwitz, Ana Ros Camacho
We construct a separable Frobenius monoidal functor from to for any subgroup of which…
Finite-dimensional quantum groups of type Super A and non-semisimple modular categories
Robert Laugwitz, Guillermo Sanmarco
We construct a series of finite-dimensional quantum groups as braided Drinfeld doubles of Nichols algebras of type Super A, for an even root of unity, and classify ribbon structure…
Constructing non-semisimple modular categories with local modules
Robert Laugwitz, Chelsea Walton
We define the class of rigid Frobenius algebras in a (non-semisimple) modular category and prove that their categories of local modules are, again, modular. This generalizes previo…
Planar diagrammatics of self-adjoint functors and recognizable tree series
Mikhail Khovanov, Robert Laugwitz
A pair of biadjoint functors between two categories produces a collection of elements in the centers of these categories, one for each isotopy class of nested circles in the plane.…
Constructing non-semisimple modular categories with relative monoidal centers
Robert Laugwitz, Chelsea Walton
This paper is a contribution to the construction of non-semisimple modular categories. We establish when Müger centralizers inside non-semisimple modular categories are also modula…
Braided commutative algebras over quantized enveloping algebras
Robert Laugwitz, Chelsea Walton
We produce braided commutative algebras in braided monoidal categories by generalizing Davydov's full center construction of commutative algebras in centers of monoidal categories.…
A categorification of cyclotomic rings
Robert Laugwitz, You Qi
For any natural number , we construct a triangulated monoidal category whose Grothendieck ring is isomorphic to the ring of cyclotomic integers .
The Relative Monoidal Center and Tensor Products of Monoidal Categories
Robert Laugwitz
This paper develops a theory of monoidal categories relative to a braided monoidal category, called augmented monoidal categories. For such categories, balanced bimodules are defin…
Comodule Algebras and 2-Cocycles over the (Braided) Drinfeld Double
Robert Laugwitz
We show that for dually paired bialgebras, every comodule algebra over one of the paired bialgebras gives a comodule algebra over their Drinfeld double via a crossed product constr…
On Fomin--Kirillov Algebras for Complex Reflection Groups
Robert Laugwitz
This note is an application of classification results for finite-dimensional Nichols algebras over groups. We apply these results to generalizations of Fomin--Kirillov algebras to…
Pointed Hopf Algebras with Triangular Decomposition -- A Characterization of Multiparameter Quantum Groups
Robert Laugwitz
In this paper, we present an approach to the definition of multiparameter quantum groups by studying Hopf algebras with triangular decomposition. Classifying all of these Hopf alge…
Braided Drinfeld and Heisenberg Doubles
Robert Laugwitz
In this paper, the Drinfeld center of a monoidal category is generalized to a class of mixed Drinfeld centers. This gives a unified picture for the Drinfeld center and a natural He…