Results 81 to 90 of about 272,600 (222)

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real‐World Data

Advanced Intelligent Discovery, Volume 2, Issue 5, October 2026.
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
wiley   +1 more source

Non-abelian extensions of Lie triple systems and Wells exact sequences [PDF]

In this paper, we investigate non-abelian extensions and inducibility of pairs of automorphisms of Lie triple systems. First, we introduce non-abelian cohomology groups and classify non-abelian extensions in terms of non-abelian cohomology groups.
Qinxiu Sun, Shuangjian Guo
core   +3 more sources

Hearing the Serre Invariant of a Compact p‐Adic Analytic Manifold

Mathematische Nachrichten, Volume 299, Issue 10, Page 3126-3138, October 2026.
ABSTRACT Using a previous novel way of defining kernel functions for Laplacian integral operators on a compact p$p$‐adic analytic manifold X$X$, one such operator Δ0s$\Delta _0^s$ with s∈R$s\in \mathbb {R}$ is applied to hearing the Serre invariant i(X)$i(X)$ by showing that a wavelet eigenvalue (with the wavelet having small support) is always ...
Patrick Erik Bradley, Ángel Morán Ledezma   +1 more
wiley   +1 more source

Foundations of Wilson Lines and Loops From Basic Concepts to Gauge Field Reconstruction

Fortschritte der Physik, Volume 74, Issue 10, October 2026.
Wilson lines and Wilson loops are reviewed as parallel transport observables in continuum gauge theory. Full holonomy data recover the local connection and curvature through short segment and small loop limits. Traced Wilson loops are gauge invariant but lose matrix information, so reconstruction requires a compatible lift constrained by trace ...
Shokoufe Faraji
wiley   +1 more source

Abelian Extensions of Modified λ-Differential Left-Symmetric Algebras and Crossed Modules

Axioms
In this paper, we define a cohomology theory of a modified λ-differential left-symmetric algebra. Moreover, we introduce the notion of modified λ-differential left-symmetric 2-algebras, which is the categorization of a modified λ-differential left ...
Fuyang Zhu, Taijie You, Wen Teng
doaj   +1 more source

Mixed motives and linear forms in the Catalan constant

Journal of the London Mathematical Society, Volume 114, Issue 4, October 2026.
Abstract We first give a geometric construction of a two‐dimensional mixed motive over Q${\mathbb {Q}}$ with the Catalan constant G=1−1/32+1/52−1/72+⋯${\mathbf {G}}=1-1/3^2+1/5^2-1/7^2+\cdots$ as a period. We then use this motive to obtain a supply of linear forms in 1 and G${\mathbf {G}}$.
Payman Eskandari, V. Kumar Murty, Yusuke Nemoto   +2 more
wiley   +1 more source

The Boolean spectrum of a Grothendieck category

Journal of the London Mathematical Society, Volume 114, Issue 4, October 2026.
Abstract A notion of support for objects in any Grothendieck category is introduced. This is based on the spectral category of a Grothendieck category and uses its Boolean lattice of localising subcategories. The support provides a classification of all subcategories that are closed under arbitrary coproducts, subobjects, and essential extensions ...
Henning Krause
wiley   +1 more source

Splitting of extensions in the category of locally compact abelian groups [PDF]

International Journal of Group Theory, 2014
Let $pounds$ be the category of all locally compact abelian (LCA) groups. In this paper, the groups $G$ in $pounds$ are determined such that every extension $0to Xto Yto Gto 0$ with divisible, $sigma-$compact $X$ in $pounds$ splits. We also determine the
Hossein Sahleh , Akbar Alijani
doaj  

Bordered Floer homology, handlebody detection, and compressing diffeomorphisms

Journal of the London Mathematical Society, Volume 114, Issue 4, October 2026.
Abstract We show that, up to connected sums with integer homology L$L$‐spaces, bordered Floer homology detects handlebodies, as well as whether a mapping class extends over a given handlebody or compression body. Using this, we combine ideas of Casson–Long with the theory of train tracks to give an algorithm using bordered Floer homology to detect ...
Akram Alishahi, Robert Lipshitz
wiley   +1 more source

bk$b^k$‐Algebroids and the variety of foliation jets

Journal of the London Mathematical Society, Volume 114, Issue 4, October 2026.
Abstract We introduce and classify singular foliations of bk+1$b^{k+1}$‐type, which formalize the properties of vector fields that are tangent to a submanifold W⊂M$W \subset M$ to order k$k$. When W$W$ is a hypersurface, these structures are Lie algebroids generalizing the bk+1$b^{k+1}$‐tangent bundles introduced by Scott.
Francis Bischoff, Álvaro del Pino, Aldo Witte   +2 more
wiley   +1 more source