Related papers: Decomposition Theory
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
The notion of random self-decomposability is generalized here. Its relation to self-decomposability, Harris infinite divisibility and its connection with a stationary first order generalized autoregressive model are presented. The notion is…
We give a diagrammatic summary of the connections between various theorems and conjectures about the vanishing of the Euler characteristic.
In this paper, we prove some foundational results on the deformation theory of E-infinity ring spectra.
The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…
A new approach to disintegration of measures is presented, allowing one to drop the usually taken separability assumption. The main tool is a result on fibers in the spectrum of algebra of essentially bounded functions established recently…
We prove two theorems on the locally finite decompositions of the cones of divisors by the cones which correspond to canonical and minimal models. We introduce the concept of the numerical linear systems in order to simplify the argument on…
We prove explit formulas for the decomposition of a differential graded Lie algebra into a minimal and a linear $L_\infty$-algebra. We define a category of metric $L_\infty$-algebras, called Palamodov $L_\infty$ algebras, where the…
In this paper, we introduce cohomology of n-Hom-Liebniz algebra morphisms and formal deformation theory of n-Hom-Liebniz algebra morphisms .
We discuss arithmetic and Hodge-theoretic properties of the isomorphisms appearing in the decomposition theorem for quantum cohomology of blowups. These properties underpin the application to the rationality questions by…
We introduce a new topological descriptor of a network called the density decomposition which is a partition of the nodes of a network into regions of uniform density. The decomposition we define is unique in the sense that a given network…
We consider a general concept of composition and decomposition of objects, and discuss a few natural properties one may expect from a reasonable choice thereof. It will be demonstrated how this leads to multiplication and co- multiplication…
In these notes we give a brief introduction to decomposition theory and we summarize some classical and well-known results. The main question is that if a partitioning of a topological space (in other words a decomposition) is given, then…
In this article, we introduce equivariant formal deformation theory of associative algebra morphisms. We introduce an equivariant deformation cohomology of associative algebra morphisms and using this we study the equivariant formal…
A constructive method for decomposing finite dimensional representations of semisimple real Lie algebras is developed. The method is illustrated by an example. We also discuss an implementation of the algorithm in the language of the…
Over the past few years, it is gradually understood that de Rham Cohomology Theory is closely related to Saint-Venant's compatibility condition in the Elasticity Theory. In this article, we will discuss the Hodge Theory and de Rham…
We describe, in terms of generators and relations, the reduction algebra, related to the diagonal embedding of the Lie algebra $\gl_n$ into $\gl_n\oplus\gl_n$. Its representation theory is related to the theory of decompositions of tensor…
In a recent article, we gave a full characterization of matrices that can be decomposed as a linear combination of two idempotents with prescribed coefficients. In this one, we use those results to improve on a recent theorem of V.…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
Consider a Leibniz superalgebra $\mathfrak L$ additionally graded by an arbitrary set $I$ (set grading). We show that $\mathfrak L$ decomposes as the sum of well-described graded ideals plus (maybe) a suitable linear subspace. In the case…