Tootfinder

Coxeter-Dynkin algebras of canonical type
Daniel Perniok
https://arxiv.org/abs/2509.17887 https://arxiv.org/pdf/2509.17887…

Coxeter-Dynkin algebras of canonical type
We propose a definition of Coxeter-Dynkin algebras of canonical type generalising the definition as a path algebra of a quiver. Moreover, we construct two tilting objects over the squid algebra - one via generalised APR-tilting and one via one-point-extensions and reflection functors - and identify their endomorphism algebras with the Coxeter-Dynkin algebra. This shows that our definition gives another representative in the derived equivalence class of the squid algebra, and hence of the corres…

from my link log —
Algebraic effects for the rest of us.
https://overreacted.io/algebraic-effects-for-the-rest-of-us/
saved 2019-07-24 ht…

Algebraic Effects for the Rest of Us — overreacted
They’re not burritos.

Jordan homomorphisms of triangular algebras over noncommutative algebras
Oksana Bezushchak
https://arxiv.org/abs/2509.17090 https://arxiv.org/pdf/2509.1709…

Jordan homomorphisms of triangular algebras over noncommutative algebras
D. Benkovič described Jordan homomorphisms of algebras of triangular matrices over a commutative unital ring without additive $2$-torsion. We extend this result to the case of noncommutative rings and remove the assumption of additive torsion. Let $R$ be an associative unital algebra over a commutative unital ring $Φ$. Consider the algebra $T_n(R)$ of triangular $n \times n$ matrices over $R$, and its subalgebra $T_n^0(R)$ consisting of matrices whose main diagonal entries lie in $Φ$. We p…

Higher Spherical Scissors Congruence I: Hopf Algebra
Inbar Klang, Josefien Kuijper, Cary Malkiewich, David Mehrle, Thor Wittich
https://arxiv.org/abs/2509.18009 https://

Higher Spherical Scissors Congruence I: Hopf Algebra
In the study of the generalization of Hilbert's Third Problem to spherical geometry, Sah constructed a Hopf algebra of spherical polytopes with product given by join and coproduct given by a generalized Dehn invariant. Using Zakharevich's reinterpretation of scissors congruence via algebraic K-theory, we lift the Sah algebra to an $(E_\infty, E_1)$-Hopf algebra spectrum whose $π_0$ is the classical Sah algebra. As an application, we show that the reduced spherical scissors congruence $K$-theor…

Commutativity of operator algebras
David P. Blecher
https://arxiv.org/abs/2509.17673 https://arxiv.org/pdf/2509.17673…

Commutativity of operator algebras
We call an operator algebra A reversible if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the symmetric operator algebras: the subalgebras of B(H) on which the transpose map is a complete isometry. In previous work we studied the unital case, where reversibility is equivalent to commutativity. We give many sufficient conditions under which a nonunital reversible or symmetric oper…

I wish more countries followed their lead.
@… https://channels.im/@alojapan/115759185890874911

Alo Japan (@alojapan@channels.im)
Attached: 1 image https://www.alojapan.com/1431434/japanese-lawmakers-support-continued-ban-on-sports-betting/ Japanese Lawmakers Support Continued Ban on Sports Betting #Japan #JapanNews #Japanese #JapaneseNews #news The Yomiuri ShimbunFormer Prime Minister Taro Aso, center, delivers his address about sports betting at a meeting in the Diet Building in Tokyo on Tuesday. By Keita Kudo / Yomiuri Shimbun Sports Writer 2:00 JST, December 22, 2025 A suprapartisan group of Diet members focuse…

Double Yangians and lattice quantum vertex algebras
Fei Kong, Haisheng Li
https://arxiv.org/abs/2509.16592 https://arxiv.org/pdf/2509.16592

Double Yangians and lattice quantum vertex algebras
For any simply-laced GCM $A$, a $\mathbb C[[\hbar]]$-algebra $\widehat{\mathcal{DY}}(A)$ was introduced in [KL1], where it was proved that the universal vacuum $\widehat{\mathcal{DY}}(A)$-module ${\mathcal{V}}_A(\ell)$ for any fixed level $\ell$ is naturally an $\hbar$-adic weak quantum vertex algebra. Let $L$ be the root lattice of $\mathfrak g(A)$. As the main results of this paper, we construct an $\hbar$-adic quantum vertex algebra $V_L[[\hbar]]^η$ as a formal deformation of the lattice ve…

Differential Privacy for Euclidean Jordan Algebra with Applications to Private Symmetric Cone Programming
Zhao Song, Jianfei Xue, Lichen Zhang
https://arxiv.org/abs/2509.16915 h…

Differential Privacy for Euclidean Jordan Algebra with Applications to Private Symmetric Cone Programming
In this paper, we study differentially private mechanisms for functions whose outputs lie in a Euclidean Jordan algebra. Euclidean Jordan algebras capture many important mathematical structures and form the foundation of linear programming, second-order cone programming, and semidefinite programming. Our main contribution is a generic Gaussian mechanism for such functions, with sensitivity measured in $\ell_2$, $\ell_1$, and $\ell_\infty$ norms. Notably, this framework includes the important ca…

The Many Faces of Non-invertible Symmetries
Shadi Ali Ahmad, Marc S. Klinger, Yifan Wang
https://arxiv.org/abs/2509.18072 https://arxiv.org/pdf/2509.18072

The Many Faces of Non-invertible Symmetries
We investigate the interplay between algebraic and categorical notions of non-invertible symmetries. In particular, a fusion categorical symmetry $\mathcal{C}$ is shown to induce an algebraic symmetry encoded in a weak Hopf algebra $H$ which is Tannaka-Krein dual to $\mathcal{C}$ in the sense that $\mathcal{C} = \text{Rep}(H^*)$. The latter duality is not unique, and consequently the algebraic symmetry acts on an extended system relative to the categorical one. We present an approach to analyzi…

Obstruction sequences to homotopy equivalences
Coline Emprin
https://arxiv.org/abs/2509.17895 https://arxiv.org/pdf/2509.17895

Obstruction sequences to homotopy equivalences
We develop an obstruction theory for the existence of gauge equivalences in complete differential graded Lie algebras. Specifically, this theory provides a characterization of homotopy equivalences between differential graded algebras governed by operads or properads, potentially colored in a groupoid. We apply this framework to establish new homotopy equivalence results in both algebraic topology and algebraic geometry, with a particular focus on the study of minimal models for highly connecte…