Related papers: Decomposition Theory
We investigate the relation between multilinear mappings and multipartite states. We show that the isomorphism between multilinear mapping and tensor product completely characterizes decomposable multipartite states in a mathematically…
[Note to the reader: properties (C2) and (C2)* are under development, in order to form a generalization of (C3) and (C3)*]
On the basis of Sz. Nagy-Foia\c{s}-Langer and von Neumann-Wold decompositions, two decompositions for dissipative linear relations are given and they are realized by transforming invariant subspaces for contractions, by means of the Z…
We develop deformation theory of algebras over quadratic operads where the parameter space is a commutative local algebra. We also give a construction of a distinguised deformation of an algebra over a quadratic operad with a complete local…
Decomposition classes provide a way of partitioning the Lie algebras of an algebraic group into equivalence classes based on the Jordan decomposition. In this paper, we investigate the decomposition classes of the Lie algebras of connected…
We begin the study of the representation theory of the infinite Temperley-Lieb algebra. We fully classify its finite dimensional representations, then introduce infinite link state representations and classify when they are irreducible or…
In this note, we study a factorization result for graded decomposition maps associated with the specializations of graded algebras. We obtain results previously known only in the ungraded setting.
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems. A major benefit of our presentation is a rigorous description of entanglement of formation. In particular,…
In this paper, we define a new cohomology theory for multiplicative Hom-pre-Lie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one by considering the structure map. We develop…
In this article, we introduce a new cohomology theory associated to a Lie 2-algebras. This cohomology theory is shown to extend the classical cohomology theory of Lie algebras; in particular, we show that the second cohomology group…
This paper applies the decomposition theorem in intersection cohomology to geometric invariant theory quotients, relating the intersection cohomology of the quotient to that of the semistable points for the action. Suppose a connected…
The Integration Theory of Linear Ordinary Differential Equation.
We show that all the tangles in a finite graph or matroid can be distinguished by a single tree-decomposition that is invariant under the automorphisms of the graph or matroid. This comes as a corollary of a similar decomposition theorem…
The singular value decomposition is arguably one of the most fundamental results in linear algebra. While rigorous proof of this result is of importance, equally important is the motivation in the applied settings. We provide a lively and…
We consider decoupling in the context of an effective quantum field theory of two scalar fields with well separated mass scales and a $Z_2\times Z_2$ symmetry. We first prove, using Wilson's exact renormalization group equation, that the…
Let $\mathbb V$ be an arbitrary linear space and $f:\mathbb V \times \ldots \times \mathbb V \to \mathbb V$ an $n$-linear map. It is proved that, for each choice of a basis ${\mathcal B}$ of $\mathbb V$, the $n$-linear map $f$ induces a…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. Morphism of the representation is the map that conserve the structure of the representation. Exploring of morphisms of the…
We describe an algorithm to decompose rational functions from which we determine the poset of groups fixing these functions.
The main goal of this paper is to develop the structure theory of Hom-Lie superalgebras in characteristic 2. We discuss their representations, semidirect product, $\alpha^k$-derivations and provide a classification in low dimension. We…
The deformation theory of Lie-Yamaguti algebras is developed by choosing a suitable cohomology. The relationship between the deformation and the obstruction of Lie-Yamaguti algebras is obtained.