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Green and Schroll give an easy criterion for a monomial algebra $A$ to be quasi-hereditary with respect to some partial order $\leq_A$. A natural follow-up question is under which conditions a monomial quasi-hereditary algebra $(A, \leq_A)$…

Representation Theory · Mathematics 2025-04-03 Anna Rodriguez Rasmussen

We prove an almost sure central limit theorem on the Poisson space, which is perfectly tailored for stabilizing functionals emerging in stochastic geometry. As a consequence, we provide almost sure central limit theorems for $(i)$ the total…

Probability · Mathematics 2019-12-16 Giovanni-Luca Torrisi , Emilio Leonardi

Almost Lie algebroids are generalizations of Lie algebroids, when the Jacobiator is not necessary null. A simple example is given, for which a Lie algebroid bracket or a Courant bundle is not possible for the given anchor, but a natural…

Differential Geometry · Mathematics 2019-03-21 Marcela Popescu , Paul Popescu

In this paper, we study the relation between the uniform Roe algebra and the uniform quasi-local algebra associated to a metric space of bounded geometry. In the process, we introduce a weakening of the notion of expanders, called…

Operator Algebras · Mathematics 2020-04-02 Kang Li , Piotr Nowak , Ján Špakula , Jiawen Zhang

The first goal of this paper is to provide an abstract framework in which to formulate and study local duality in various algebraic and topological contexts. For any stable $\infty$-category $\mathcal{C}$ together with a collection of…

Algebraic Topology · Mathematics 2019-01-23 Tobias Barthel , Drew Heard , Gabriel Valenzuela

We describe certain almost-simple algebraic supergroups over an algebraically closed field of odd or zero characteristic. In addition to supergroups with simple Lie superalgebras from Kac's theorem, we construct new supergroups whose Lie…

Rings and Algebras · Mathematics 2025-11-21 S. Bouarroudj , A. N. Zubkov

Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but…

Probability · Mathematics 2009-09-29 Michael Hardy

Qualitative calculi play a central role in representing and reasoning about qualitative spatial and temporal knowledge. This paper studies distributive subalgebras of qualitative calculi, which are subalgebras in which (weak) composition…

Artificial Intelligence · Computer Science 2015-06-02 Zhiguo Long , Sanjiang Li

A new class of completely integrable models is constructed. These models are deformations of the famous integrable and exactly solvable Gaudin models. In contrast with the latter, they are quasi-exactly solvable, i.e. admit the algebraic…

High Energy Physics - Theory · Physics 2009-10-30 Alexander Ushveridze

A double algebra is a linear space $V$ equipped with linear map $V\otimes V\to V\otimes V$. Additional conditions on this map lead to the notions of Lie and associative double algebras. We prove that simple finite-dimensional Lie double…

Quantum Algebra · Mathematics 2018-10-31 M. E. Goncharov , P. S. Kolesnikov

We realize the relative discrete series of a weighted $L^2$-space on a bounded symmetric doamin as kernels of invariant Cauchy-Riemann operator, and thus as the spaces of nearly holomorphic functions.

Representation Theory · Mathematics 2007-05-23 Genkai Zhang

We consider the problem of classifying gradings by groups on a finite-dimensional algebra $A$ (with any number of multilinear operations) over an algebraically closed field. We introduce a class of gradings, which we call almost fine, such…

Rings and Algebras · Mathematics 2025-06-24 Alberto Elduque , Mikhail Kochetov

We give a new proof of a theorem of Kleiner-Leeb: that any quasi-isometrically embedded Euclidean space in a product of symmetric spaces and Euclidean buildings is contained in a metric neighborhood of finitely many flats, as long as the…

Geometric Topology · Mathematics 2009-02-26 Kevin Wortman

We give numerous examples of almost Lie algebroids arising as Dirac structures in pre-Courant algebroids, e.g. from twisted Poisson structures, as well as from twisted actions of a Lie algebra. We moreover define a cohomology for them,…

Differential Geometry · Mathematics 2012-06-26 Melchior Grützmann , Xiaomeng Xu

We prove a characterization of profinite algebras, i.e., topological algebras that are isomorphic to a projective limit of finite discrete algebras. In general profiniteness concerns both the topological and algebraic characteristics of a…

Logic · Mathematics 2020-08-25 Friedrich Martin Schneider , Jens Zumbrägel

We have defined almost separable space. We show that like separability, almost separability is $c$ productive and converse also true under some restrictions. We establish a Baire Category theorem like result in Hausdorff, Pseudocompacts…

General Topology · Mathematics 2020-02-13 Sagarmoy Bag , Ram Chandra Manna , Sourav Kanti Patra

A subalgebra of a semisimple Lie algebra is wide if every simple module of the semisimple Lie algebra remains indecomposable when restricted to the subalgebra. A subalgebra is narrow if the restrictions of all non-trivial simple modules to…

Representation Theory · Mathematics 2024-03-28 Andrew Douglas , Joe Repka

Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none…

Logic in Computer Science · Computer Science 2021-12-10 Oliver Nash

We systematically develop analogs of basic concepts from classical descriptive set theory in the context of pointless topology. Our starting point is to take the elements of the free complete Boolean algebra generated by the frame…

Logic · Mathematics 2020-11-03 Ruiyuan Chen

We study topological median algebra structures on Euclidean spaces and, more generally, ER homology manifolds. We show that all such median structures have a local CAT(0) cubulation structure. We also show that topological median algebra…

Geometric Topology · Mathematics 2025-12-11 Mladen Bestvina , Kenneth Bromberg , Michah Sageev
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