Outputs (16)

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. (in press). The braids on your blanket. Journal of Humanistic Mathematics,

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.

A categorification of cyclotomic rings (2023)
Journal Article
Laugwitz, R., & Qi, Y. (2023). A categorification of cyclotomic rings. Quantum Topology, 13(3), 539-577. https://doi.org/10.4171/qt/172

For any natural number n≥2, we construct a triangulated monoidal category whose Grothendieck ring is isomorphic to the ring of cyclotomic integers On​. This construction provides an affirmative resolution to a problem raised by Khovanov in 2005.

The indecomposable objects in the center of Deligne's category Rep St (2023)
Journal Article
Flake, J., Harman, N., & Laugwitz, R. (2023). The indecomposable objects in the center of Deligne's category Rep St. Proceedings of the London Mathematical Society, 126(4), 1134-1181. https://doi.org/10.1112/plms.12509

We classify the indecomposable objects in the monoidal center of Deligne's interpolation category Rep St by viewing Rep St as a model‐theoretic limit in rank and characteristic. We further prove that the center of Rep St is semisimple if and only if... Read More about The indecomposable objects in the center of Deligne's category Rep St.

Constructing Non-Semisimple Modular Categories with Relative Monoidal Centers (2021)
Journal Article
Laugwitz, R., & Walton, C. (2022). Constructing Non-Semisimple Modular Categories with Relative Monoidal Centers. International Mathematics Research Notices, 2022(20), 15826-15868. https://doi.org/10.1093/imrn/rnab097

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 modular. As a consequence, we obtain conditions under which relative monoida... Read More about Constructing Non-Semisimple Modular Categories with Relative Monoidal Centers.

On the monoidal center of Deligne's category Re̲p(St) (2020)
Journal Article
Flake, J., & Laugwitz, R. (2021). On the monoidal center of Deligne's category Re̲p(St). Journal of the London Mathematical Society, 103(3), 1153-1185. https://doi.org/10.1112/jlms.12403

We explicitly compute a monoidal subcategory of the monoidal center of Deligne’s interpolation category Rep(St), for t not necessarily a natural number, and we show that this subcategory is a ribbon category. For t = n, a natural number, there exists... Read More about On the monoidal center of Deligne's category Re̲p(St).

Braided commutative algebras over quantized enveloping algebras (2020)
Journal Article
Laugwitz, R., & Walton, C. (2021). Braided commutative algebras over quantized enveloping algebras. Transformation Groups, 26, 957-993. https://doi.org/10.1007/s00031-020-09599-9

We produce braided commutative algebras in braided monoidal categories by generalizing Davydov's full center construction of commutative algebras in centers of monoidal categories. Namely, we build braided commutative algebras in relative monoidal ce... Read More about Braided commutative algebras over quantized enveloping algebras.