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The unified product was defined in \cite{am3} related to the restricted extending structure problem for Hopf algebras: a Hopf algebra $E$ factorizes through a Hopf subalgebra $A$ and a subcoalgebra $H$ such that $1\in H$ if and only if $E$…

Rings and Algebras · Mathematics 2014-02-24 A. L. Agore , G. Militaru

We define a new class of irreducible groups, called groups not infinite-index presentable by products or not IIPP. We prove that certain aspherical manifolds with fundamental groups not IIPP do not admit maps of non-zero degree from direct…

Geometric Topology · Mathematics 2019-09-09 Christoforos Neofytidis

We show that finite-dimensional order unit spaces equipped with a continuous sequential product as defined by Gudder and Greechie are homogeneous and self-dual. As a consequence of the Koecher-Vinberg theorem these spaces therefore…

Quantum Physics · Physics 2020-12-16 John van de Wetering

We study the construction of tensor products of representations up to homotopy, which are the A-infinity version of ordinary representations. We provide formulas for the construction of tensor products of representations up to homotopy and…

Algebraic Topology · Mathematics 2010-09-30 Camilo Arias Abad , Marius Crainic , Benoit Dherin

Finite topological spaces are in bijective correspondence with preorders on finite sets. We undertake their study using combinatorial tools that have been developed to investigate general discrete structures. A particular emphasis will be…

Algebraic Topology · Mathematics 2015-09-04 Loïc Foissy , Claudia Malvenuto , Frédéric Patras

We present a systematic study of the structure of crossed products and fixed point algebras by compact group actions with the Rokhlin property on not necessarily unital C*-algebras. Our main technical result is the existence of an…

Operator Algebras · Mathematics 2016-05-31 Eusebio Gardella

We analyse volume-preserving actions of product groups on Riemannian manifolds. To this end, we establish a new superrigidity theorem for ergodic cocycles of product groups ranging in linear groups. There are no a priori assumptions on the…

Group Theory · Mathematics 2019-12-19 Alex Furman , Nicolas Monod

Motivated by some alternatives to the classical logical model of boolean algebra, this paper deals with algebraic structures which extend skew lattices by locally invertible elements. Following the meme of the Ehresmann-Schein-Nambooripad…

Group Theory · Mathematics 2021-01-07 D. G. FitzGerald

Birkhoff's representation theorem for finite distributive lattices states that any finite distributive lattice is isomorphic to the lattice of order ideals (lower sets) of the partial order of the join-irreducible elements of the lattice.…

Combinatorics · Mathematics 2023-03-15 Dale R. Worley

Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…

Category Theory · Mathematics 2008-02-06 Claudio Pisani

Ultraproducts are a well-known tool in the classical model theory of first-order logic. We explore their uses in the context of finite model theory.

Logic · Mathematics 2013-10-14 Philip Dittmann

We provide a detailed study of actions of the integers on compact quantum metric spaces, which includes general criteria ensuring that the associated crossed product algebra is again a compact quantum metric space in a natural way. We…

Operator Algebras · Mathematics 2021-07-01 Jens Kaad , David Kyed

Let $\mathbf D$ be the set of isomorphism types of finite double partially ordered sets, that is sets endowed with two partial orders. On $\BZ\mathbf D$ we define a product and a coproduct, together with an internal product, that is,…

Representation Theory · Mathematics 2011-02-19 Claudia Malvenuto , Christophe Reutenauer

We introduce the category of C*-discrete inclusions of C*-algebras $A\subset B$ with a faithful conditional expectation $E:B\twoheadrightarrow A$. This class includes many examples such as finite Watatani index inclusions, and also abundant…

Operator Algebras · Mathematics 2026-01-06 Roberto Hernández Palomares , Brent Nelson

We classify the finite groups $G$ such that the group of units of the integral group ring ${\mathbb Z} G$ has a subgroup of finite index which is a direct product of free-by-free groups.

Group Theory · Mathematics 2007-05-23 Eric Jespers , Antonio Pita , Angel del Rio , Manuel Ruiz , Pavel Zalesski

We construct combinatorial model category structures on the categories of (marked) categories and (marked) pre-additive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of…

Algebraic Topology · Mathematics 2021-05-28 Ulrich Bunke , Alexander Engel , Daniel Kasprowski , Christoph Winges

Let $f\colon M\to N$ be a continuous map between closed irreducible graph manifolds with infinite fundamental group. Perron and Shalen showed that if $f$ induces a homology equivalence on all finite covers, then $f$ is in fact homotopic to…

Geometric Topology · Mathematics 2010-04-22 Matthias Aschenbrenner , Stefan Friedl

Let $\mathcal C$ be the category of finite graphs. Lov\`{a}sz shows that the semi-ring of isomorphism classes of $\mathcal C$ (with coproduct as sum, and product as multiplication) is embedded into the direct product of the semi-ring of…

Category Theory · Mathematics 2022-07-14 Shoma Fujino , Makoto Matsumoto

We give a rigorous formulation of the intuitive idea that a differentiable map should be thesame thing as a locally, or infinitesimally, linear map: just as a linear map respects the operations of addition and multiplication by scalars ina…

Category Theory · Mathematics 2015-07-24 Wolfgang Bertram

We consider infinite $\Z_\Z$-index complexes $\mathcal C$ of spaces with elements depending on a number of parameters, complete with respect to a linear associative regular inseparable multilinear product. The existence of nets of vanishing…

Functional Analysis · Mathematics 2026-03-06 Daniel Levin , Alexander Zuevsky
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