Outputs (22)

Presentations for small reflection equation algebras of type A (2025)
Journal Article
Cooke, J., & Laugwitz, R. (2025). Presentations for small reflection equation algebras of type A. Journal of Algebra, 682, 131-187. https://doi.org/10.1016/j.jalgebra.2025.05.037

We give presentations, in terms of the generators and relations, for the reflection equation algebras of type GLn and SLn, i.e., the covariantized algebras of the dual Hopf algebras of the small quantum groups of gln and sln. Our presentations displa... Read More about Presentations for small reflection equation algebras of type A.

Reflective centers of module categories and quantum K-matrices (2025)
Journal Article
Laugwitz, R., Walton, C., & Yakimov, M. (2025). Reflective centers of module categories and quantum K-matrices. Forum of Mathematics, Sigma, 13, Article e95. https://doi.org/10.1017/fms.2025.10055

Our work is motivated by obtaining solutions to the quantum reflection equation (qRE) by categorical methods. To start, given a braided monoidal category C and C-module category M, we introduce a version of the Drinfeld center ZpCq of C adapted for M... Read More about Reflective centers of module categories and quantum K-matrices.

Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers (2025)
Journal Article
Flake, J., Laugwitz, R., & Posur, S. (2025). Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers. Advances in Mathematics, 475, Article 110344. https://doi.org/10.1016/j.aim.2025.110344

We identify general conditions, formulated using the projection formula morphisms, for a functor that is simultaneously left and right adjoint to a strong monoidal functor to be a Frobenius monoidal functor. Moreover, we identify stronger conditions... Read More about Frobenius monoidal functors from ambiadjunctions and their lifts to Drinfeld centers.

Pretriangulated 2-representations via dg algebra 1-morphisms (2025)
Journal Article
Laugwitz, R., & Miemietz, V. (in press). Pretriangulated 2-representations via dg algebra 1-morphisms. Documenta Mathematica,

This paper develops a theory of pretriangulated 2-representations of dg 2-categories. We characterize cyclic pretriangulated 2-representations, under certain compactness assumptions, in terms of dg modules over dg algebra 1-morphisms internal to asso... Read More about Pretriangulated 2-representations via dg algebra 1-morphisms.

Infinitesimal 2-braidings from 2-shifted Poisson structures (2025)
Journal Article
Kemp, C., Laugwitz, R., & Schenkel, A. (2025). Infinitesimal 2-braidings from 2-shifted Poisson structures. Journal of Geometry and Physics, 212, Article 105456. https://doi.org/10.1016/j.geomphys.2025.105456

It is shown that every 2-shifted Poisson structure on a finitely generated semi-free commutative differential graded algebra A defines a very explicit infinitesimal 2-braiding on the homotopy 2-category of the symmetric monoidal dg-category of finite... Read More about Infinitesimal 2-braidings from 2-shifted Poisson structures.

Differential graded cell 2-representations (2025)
Journal Article
Laugwitz, R., & Miemietz, V. (in press). Differential graded cell 2-representations. Arkiv för Matematik,

This article develops a theory of cell combinatorics and cell 2-representations for differential graded 2-categories. We introduce two types of partial preorders, called the strong and weak preorder. We then analyse and compare them. The weak preorde... Read More about Differential graded cell 2-representations.

The Braids on Your Blanket (2024)
Journal Article
Cheng, M., & Laugwitz, R. U. (2024). The Braids on Your Blanket. Journal of Humanistic Mathematics, 14(2), 286-337. https://doi.org/10.5642/jhummath.YMZO2460

In this expositional essay, we introduce some elements of the study of groups by analysing the braid pattern on a knitted blanket. We determine that the blanket features pure braids with a minimal number of crossings. Moreover, we determine polynomia... Read More about The Braids on Your Blanket.

Planar diagrammatics of self-adjoint functors and recognizable tree series (2023)
Journal Article
Khovanov, M., & Laugwitz, R. (2023). Planar diagrammatics of self-adjoint functors and recognizable tree series. Pure and Applied Mathematics Quarterly, 19(5), 2409-2499. https://doi.org/10.4310/pamq.2023.v19.n5.a4

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. If the centers are equipped with a trace map into the ground field, t... Read More about Planar diagrammatics of self-adjoint functors and recognizable tree series.

Constructing Non-semisimple Modular Categories with Local Modules (2023)
Journal Article
Laugwitz, R., & Walton, C. (2023). Constructing Non-semisimple Modular Categories with Local Modules. Communications in Mathematical Physics, 403, 1363-1409. https://doi.org/10.1007/s00220-023-04824-4

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 previous work of Kirillov and Ostrik (Adv Math 171(2):183–227, 2002) in the... Read More about Constructing Non-semisimple Modular Categories with Local Modules.

Indecomposable objects in Khovanov–Sazdanovic's generalizations of Deligne's interpolation categories (2023)
Journal Article
Flake, J., Laugwitz, R., & Posur, S. (2023). Indecomposable objects in Khovanov–Sazdanovic's generalizations of Deligne's interpolation categories. Advances in Mathematics, 415, Article 108892. https://doi.org/10.1016/j.aim.2023.108892

Khovanov and Sazdanovic recently introduced symmetric monoidal categories parameterized by rational functions and given by quotients of categories of two-dimensional cobordisms. These categories generalize Deligne's interpolation categories of repres... Read More about Indecomposable objects in Khovanov–Sazdanovic's generalizations of Deligne's interpolation categories.