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The nonnegative matrix factorization is a widely used, flexible matrix decomposition, finding applications in biology, image and signal processing and information retrieval, among other areas. Here we present a related matrix factorization.…
The algebraic theory of third-order tensors under the $t$-product is naturally formulated over the complex field via Fourier block diagonalization. However, many applications require real-valued representations. In this paper, we…
Let $V$ be a vector space endowed with a non-degenerate quadratic form $Q$. If the base field $\mathbb{F}$ is different from $\mathbb{F}_2$, it is known that every isometry can be written as a product of reflections. In this article, we…
Factorization method is developed for a family of discretely spiked harmonic oscillators. Two sets of intertwining and ladder operators are presented to algebraically generate eigenstates with energies isomorphic to those of the ordinary…
Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…
We investigate the existence and the properties of fully separable (fully factorized) ground states in quantum spin systems. Exploiting techniques of quantum information and entanglement theory we extend a recently introduced method and…
We establish a correspondence between consistent comprehension schemes and complete orthogonal factorisation systems. The comprehensive factorisation of a functor between small categories arises in this way. Similar factorisation systems…
Modular functors are traditionally defined as systems of projective representations of mapping class groups of surfaces that are compatible with gluing. They can formally be described as modular algebras over central extensions of the…
We study the homotopy category $\mathrm{hmf}(R,W)$ of matrix factorizations of non-zero elements $W\in R^\times$, where $R$ is an elementary divisor domain. When $R$ has prime elements and $W$ factors into a square-free element $W_0$ and a…
We give an account of lax orthogonal factorisation systems on order-enriched categories. Among them, we define and characterise the KZ-reflective ones, in a way that mirrors the characterisation of reflective orthogonal factorisation…
We construct and compare two alternative quantizations, as a time-orderable prefactorization algebra and as an algebraic quantum field theory valued in cochain complexes, of a natural collection of free BV theories on the category of…
We investigate a polynomial factorization problem that naturally arises from Hartley's factorization condition on the Alexander polynomial of freely periodic knots. We give a number-theoretic interpretation of this factorization condition,…
We consider the problem of when one quandle homomorphism will factor through another, restricting our attention to the case where all quandles involved are connected. We provide a complete solution to the problem for surjective quandle…
Let $\mathcal{H} = \mathcal{H}(W,S)$ be the Hecke algebra of the Coxeter system $(W,S)$ over $\mathbb{Z}[q^{\pm1}]$, where $W$ is the Weyl group of a symmetrizable Kac-Moody algebra. In this paper, we show that the matrix of Kazhdan-Lusztig…
In a previous work we showcased the factorization method to find the symmetries of superintegrable systems with spherical separability in flat spaces. Here we analyze the same problem, but in constant curvature spaces along the examples of…
A generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in Quantum Mechanics. The method is applied in the study of radial oscillator, Morse…
We describe a relation between the invariants of $n$ ordered points in $P^d$ and of points contained in a union of linear subspaces $P^{d1}\cup P^{d2} \subset P^d$. This yields an attaching map for GIT quotients parameterizing point…
We investigate canonical factorizations of ordered functors of ordered groupoids through star-surjective functors. Our main construction is a quotient ordered groupoid, depending on an ordered version of the notion of normal subgroupoid,…
We define the twisted tensor product of two enriched categories, which generalizes various sorts of `products' of algebraic structures, including the bicrossed product of groups, the twisted tensor product of (co)algebras and the double…
In the realm of invertible symmetry, the topological approach based on classifying spaces dominates the classification of 't Hooft anomalies and symmetry protected topological phases. We explore the alternative algebraic approach based on…