Tootfinder

The Braided Prairie: Six Nebraskan Literary Voices on Land, Life, and Legacy
The American Great Plains have produced a literary tradition as vast and complex as the landscape itself. Nebraska, with its braided rivers and endless horizons, stands at the heart of this tradition, having shaped some of the nation's most distinctive literary voices. From the rolling Sandhills to the fossil-rich badlands, from pioneer settlements to Native American territories, the state's…

Generalized Yetter-Drinfeld modules, the center of bi-actegories and groupoid-crossed braided bicategories
Ryan Aziz, Joost Vercruysse
https://arxiv.org/abs/2507.08722

Generalized Yetter-Drinfeld modules, the center of bi-actegories and groupoid-crossed braided bicategories
We study the notion of the $E$-center $\mathcal{Z}_E(\mathcal{M})$ of a $(\mathcal{C}, \mathcal{D})$-biactegory (or bimodule category) $\mathcal{M}$, relative to an op-monoidal functor $E: \mathcal{C} \to \mathcal{D}$. Specializing this notion to the case $\mathcal{M} = {}_A\mathrm{Mod}$, $\mathcal{C}={}_H\mathrm{Mod}$, $\mathcal{D} = {}_K\mathrm{Mod}$, and $E \simeq C\otimes_H - : {}_H\mathrm{Mod} \to {}_K\mathrm{Mod}$, where $H$ and $K$ are bialgebras, $A$ is an $(H,K)$-bicomodule algebra and…

It's truth in advertising when the braided UHMWPE product page shows it unraveling! 🤣
I've learned that plasma lighters are great tools for cutting light gauge synthetic cord. They are basically small hot plasma knives that cut slowly. Works for UHMWPE, nylon, polyester, and more. Also PET cable sheath, which is otherwise highly motivated to spontaneously disassemble itself.

The Braided Prairie: Six Nebraskan Literary Voices on Land, Life, and Legacy
The American Great Plains have produced a literary tradition as vast and complex as the landscape itself. Nebraska, with its braided rivers and endless horizons, stands at the heart of this tradition, having shaped some of the nation's most distinctive literary voices. From the rolling Sandhills to the fossil-rich badlands, from pioneer settlements to Native American territories, the state's…

Braided Gelfand-Zetlin algebras and their semiclassical counterparts
Dimitry Gurevich, Pavel Saponov
https://arxiv.org/abs/2507.04564 https://

Braided Gelfand-Zetlin algebras and their semiclassical counterparts
We construct analogs of the Gelfand-Zetlin algebras in the Reflection Equation algebras, corresponding to Hecke symmetries, mainly to those coming from the quantum groups U_q(sl(N)). Corresponding semiclassical (i.e. Poisson) counterparts of the Gelfand-Zetlin algebras are described.

Physical implications of four dimensional braided noncommutative gravity
Milorad Be\v{z}ani\'c, Marija Dimitrijevi\'c \'Ciri\'c, Biljana Nikoli\'c, Voja Radovanovi\'c
https://arxiv.org/abs/2508.02205

Physical implications of four dimensional braided noncommutative gravity
The formulation of gravity theories on noncommutative (NC) spacetimes has been an active area of research for some time. Various models and methods have been proposed in the literature. Even within the star-product formalism, there are several distinct approaches to constructing NC deformations of General Relativity (GR) and Einstein-Cartan-Palatini (ECP) gravity. Some models are based on the NC local Lorentz symmetry, while others rely on NC deformations of the diffeomorphism symmetry of GR. I…

Semisimplicity of conformal blocks
Pierre Godfard
https://arxiv.org/abs/2507.06318 https://arxiv.org/pdf/2507.06318

Semisimplicity of conformal blocks
We prove that braid group representations associated to braided fusion categories and mapping class group representations associated to modular fusion categories are always semisimple. The proof relies on the theory of extensions in non-Abelian Hodge theory and on Ocneanu rigidity. By combining this with previous results on the existence of variations in Hodge structures, we further show that such a braid group or mapping class group representation preserves a non-degenerate Hermitian form and …

The standard construction for cocycle twisted and braided tensor product W$^*$-algebras
K. De Commer, J. Krajczok
https://arxiv.org/abs/2508.00595 https://…

The standard construction for cocycle twisted and braided tensor product W$^*$-algebras
Given a locally compact quantum group $\mathbb{G}$ and a (generalized) dual unitary $2$-cocycle $\hatΩ$, any W$^*$-algebra $A$ with a $\mathbb{G}$-action can be twisted into a new W$^*$-algebra $A_{\hatΩ}$ with an action by the cocycle twist $\mathbb{G}_{\hatΩ}$ of $\mathbb{G}$. We show how, in general, the standard space $L^2(A_{\hatΩ})$, with its standard $\mathbb{G}_{\hatΩ}$-representation, can be seen as a twist of $L^2(A)$ with its standard $\mathbb{G}$-representation. We then apply t…

On reducible Killing forms for groups of Lie type
Kevin Ivan Piterman, Charlotte Roelants
https://arxiv.org/abs/2507.17902 https://arxiv.org/pdf/2507.17902…

On reducible Killing forms for groups of Lie type
Killing forms on finite groups arise as examples of braided Killing forms on braided Lie algebras. For a finite group $G$ and a $G$-stable subset $\mathcal{C}$, the Killing form associated with $\mathbb{C}[\mathcal{C}]$ is given by $K_{\mathcal{C}}(a,b) = |C_G(ab) \cap \mathcal{C}|$ for $a,b\in \mathcal{C}$. Motivated by Cartan's criterion for semisimplicity of Lie algebras, and previous work of López Peña, Majid, and Rietsch, we study the non-degeneracy and irreducibility of $K_{\m…

Half Spatially Coupled Turbo-Like Codes
Xiaowei Wu, Lei Yang, Min Qiu, Chong Han, Jinhong Yuan
https://arxiv.org/abs/2507.01685 https://

Half Spatially Coupled Turbo-Like Codes
This paper presents a new class of spatially coupled turbo-like codes (SC-TCs), namely half spatially coupled braided convolutional codes (HSC-BCCs) and half spatially coupled parallel concatenated codes (HSC-PCCs). Different from the conventional SC-TCs, the proposed codes have simpler and deterministic coupling structures. Most notably, the coupling of HSC-BCCs is performed by re-encoding the whole coupling sequence in the component encoder of one time instant, rather than spreading the coupl…

2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging
Nils Carqueville, Benjamin Haake
https://arxiv.org/abs/2506.08178 https://

2-Group Symmetries of 3-dimensional Defect TQFTs and Their Gauging
A large class of symmetries of topological quantum field theories is naturally described by functors into higher categories of topological defects. Here we study 2-group symmetries of 3-dimensional TQFTs. We explain that these symmetries can be gauged to produce new TQFTs iff certain defects satisfy the axioms of orbifold data. In the special case of Reshetikhin-Turaev theories coming from $G$-crossed braided fusion categories $\mathcal C^\times_G$, we show that there are 0- and 1-form symmetri…

Replaced article(s) found for nlin.CD. https://arxiv.org/list/nlin.CD/new
[1/1]:
- Braided mixing in confined chiral active matter
Yue Wang, Jonas Berx
https://…

This Is Not the World I Wanted to Leave for You: Reflections on Legacy, Loss, and the Future We Shape
I have been thinking a great deal lately about living and dying, and about the strange, stubborn human hunger to leave something meaningful behind. The faces of those I have known who have already passed return to me in quiet moments, and I find myself watching those who are, even now, nearing the end of their own stories. I also include my final braided prairie knot…

This Is Not the World I Wanted to Leave for You: Reflections on Legacy, Loss, and the Future We Shape | David Boles, Blogs
I have been thinking a great deal lately about living and dying, and about the strange, stubborn human hunger to leave something meaningful behind. The faces of those I have known who have already …

Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories
Thibault D. D\'ecoppet
https://arxiv.org/abs/2506.16241 https://

Relative Invertibility and Full Dualizability of Finite Braided Tensor Categories
Fix a finite symmetric tensor category $\mathcal{E}$ over an algebraically closed field. We derive an $\mathcal{E}$-enriched version of Shimizu's characterizations of non-degeneracy for finite braided tensor categories. In order to do so, we consider, associated to any $\mathcal{E}$-enriched finite braided tensor category $\mathcal{A}$ satisfying a mild technical assumption, a Hopf algebra $\mathbb{F}_{\mathcal{E}/\mathcal{A}}$ in $\mathcal{A}$. This is a generalization of Lyubashenko's univers…

The VIBE Framework: A Student-Centered Approach to Teaching Knot Theory in Secondary Mathematics
Ioannis Diamantis
https://arxiv.org/abs/2506.22886 https:/…

The VIBE Framework: A Student-Centered Approach to Teaching Knot Theory in Secondary Mathematics
Knot theory, a visual and intuitive branch of topology, offers a unique opportunity to introduce advanced mathematical thinking in secondary education. Despite its accessibility and cross-disciplinary relevance, it remains largely absent from standard curricula. This paper proposes the {\it VIBE framework}, a student-centered approach, structured around four pedagogical pillars: Visual, Inquiry-based, Braided (collaborative), and Embedded (contextualized) learning. Rooted in constructivist theo…

Holography for bulk-boundary local topological order
Corey Jones, Pieter Naaijkens, David Penneys
https://arxiv.org/abs/2506.19969 https://

Holography for bulk-boundary local topological order
In our previous article [arXiv:2307.12552], we introduced local topological order (LTO) axioms for quantum spin systems which allowed us to define a physical boundary manifested by a net of boundary algebras in one dimension lower. This gives a formal setting for topological holography, where the braided tensor category of DHR bimodules of the physical boundary algebra captures the bulk topological order. In this article, we extend the LTO axioms to quantum spin systems equipped with a topolo…

Majorana zero modes in semiconductor-superconductor hybrid structures: Defining topology in short and disordered nanowires through Majorana splitting
Haining Pan, Sankar Das Sarma
https://arxiv.org/abs/2507.00128

Majorana zero modes in semiconductor-superconductor hybrid structures: Defining topology in short and disordered nanowires through Majorana splitting
Majorana zero modes (MZMs) are bound midgap excitations at the ends of a 1D topological superconductor, which must come in pairs. If the two MZMs in the pair are sufficiently well-separated by a distance much larger than their individual localization length, then the MZMs behave as non-Abelian anyons which can be braided to carry out fault-tolerant topological quantum computation. In this `topological' regime of well-separated MZMs, their overlap is exponentially small, leading to exponentially…

Higher degree covering moves for 3-manifolds
Aru Mukherjea
https://arxiv.org/abs/2507.15141 https://arxiv.org/pdf/2507.15141…

Higher degree covering moves for 3-manifolds
We provide a complete set of covering moves, or moves relating colored link diagrams appearing as branch sets of simple branched coverings of $S^3$ by the same 3-manifold, for each fixed degree $d \geq 4$. We also show that up to $d-2$ stabilizations, this set can be refined to two local tangle replacements. This extends prior work of Apostolakis and Piergallini, and is a braided analogue to the covering moves of Bobtcheva and Piergallini.

$\displaystyle SL(2, {\Bbb Z})$, les tresses \`a trois brins, le tore modulaire et $Aut^{ }(F_{2})$
Alexis Marin
https://arxiv.org/abs/2506.19371 https://

$\displaystyle SL(2, {\Bbb Z})$, les tresses à trois brins, le tore modulaire et $Aut^{+}(F_{2})$
The action of $SL(2, {\bf Z})$ on the integer torus and its quotient by central symmetry and Artin's presentation of three strings braid group $B_{3}$, produces a presentation with parabolic generators $\pmatrix{1& -1\cr 0& 1\cr}$ and $\pmatrix{1& 0\cr 1& 1\cr}$. This braided presentation describes the action of the derived group on Poincaré's half plane and its quotient the modular torus, just as Nielsen's theorem giving the group of direct automorphisms of the free group on two generators as…

On the finite generation of the cohomology of bosonizations
Nicol\'as Andruskiewitsch, David Jaklitsch, Van C. Nguyen, Amrei Oswald, Julia Plavnik, Anne V. Shepler, Xingting Wang
https://arxiv.org/abs/2506.05267

On the finite generation of the cohomology of bosonizations
We use deformation sequences of (Hopf) algebras, extending the results of Negron and Pevtsova, to show that bosonizations of some suitable braided Hopf algebras by some suitable finite-dimensional Hopf algebras have finitely generated cohomology. In fact, our results are shown in more generality for smash products. As applications, we prove the bosonizations of some Nichols algebras (such as Nichols algebras of diagonal type, the restricted Jordan plane, Nichols algebras of direct sums of Jorda…

This https://arxiv.org/abs/2403.10366 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A Graded Schur Lemma and a graded-monoidal structure for induced modules over graded-commutative algebras
We consider algebras and Frobenius algebras, internal to a monoidal category, that are graded over a finite abelian group. For the case that A is a twisted group algebra in a linear abelian monoidal category we obtain a graded generalization of the Schur Lemma for the category of induced A-modules. We further show that if the monoidal category is braided and A is commutative up to a bicharacter of the grading group, then the category of induced A-modules can be endowed with a graded-monoidal st…

Biproduct Quasi-Hopf Algebras of Rank 2
Daniel Bulacu, Matteo Misurati
https://arxiv.org/abs/2508.00597 https://arxiv.org/pdf/2508.00597

Biproduct Quasi-Hopf Algebras of Rank 2
Inspired by the work of Radford, for $H$ an arbitrary quasi-Hopf algebra we describe all the Hopf algebras of dimension $2$ within the braided category of left Yetter-Drinfeld modules over $H$ and determine the biproduct quasi-Hopf algebras defined by them. Classes of such biproduct quasi-Hopf algebras are obtained by taking $H$ as the Hopf algebra of functions on a group $G$, endowed with the quasi-Hopf algebra structure provided by a non-trivial $3$-cocycle on $G$ (especially when $G$ is a fi…