Related papers: Matrix factorizations for quantum complete interse…
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.
We study the representation dimension of the class of algebras known as quantum complete intersections. For such an algebra, we show that the representation dimension is at most twice its codimension. Moreover, we show that the…
We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split…
Factorization of matrices of Laurent polynomials plays an important role in mathematics and engineering such as wavelet frame construction and filter bank design. Wavelet frames (a.k.a. framelets) are useful in applications such as signal…
We construct a minimal projective bimodule resolution for every finite dimensional quantum complete intersection of codimension two. Then we use this resolution to compute both the Hochschild cohomology and homology for such an algebra. In…
Euclidean distance matrices corresponding to an arithmetic progression have rich spectral and structural properties. We exploit those properties to develop completely positive factorizations of translations of those matrices. We show that…
We find a connection between the existence of a factorization of a quantum channel and the existence of low-rank solutions to certain linear matrix equations. Using this, we show that if a quantum channel is factorized by a direct integral…
We study a numerical semigroup ring as an algebra over another numerical semigroup ring. The complete intersection property of numerical semigroup algebras is investigated using factorizations of monomials into minimal ones. The goal is to…
The aim of this paper is to introduce and study a large class of $\mathfrak{g}$-module algebras which we call factorizable by generalizing the Gauss factorization of (square or rectangular) matrices. This class includes coordinate algebras…
We calculate factorizing twists in evaluation representations of the quantum affine algebra U_q(\hat sl_2). From the factorizing twists we derive a representation independent expression of the R-matrices of U_q(\hat sl_2). Comparing with…
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
New algorithms for prime factorization that outperform the existing ones or take advantage of particular properties of the prime factors can have a practical impact on present implementations of cryptographic algorithms that rely on the…
In [2] a new factorization for infinite Hessenberg banded matrices was introduced. In this note we prove that this kind of factorization can also be used for finite matrices. In addition, a new method for solving banded linear systems is…
We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…
We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex…
We introduce the Mixed-Integer Quadratically Constrained Quadratic Programming framework for the quantum compilation problem and apply it in the context of topological quantum computing. In this setting, quantum gates are realized by…
Several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded $k$-algebra; these notions are justified by examples from noncommutative invariant theory.
We give an interpretation of the semi-infinite intersection cohomology sheaf associated to a semisimple simply-connected algebraic group in terms of finite-dimensional geometry. Specifically, we describe a procedure for building…
We propose a generalization of the factorization method to the case when $\mathcal{G}$ is a finite dimensional Lie algebra such that $\mathcal{G}=\mathcal{G}_0\oplus M \oplus N$ (direct sum of vector spaces), where $\mathcal{G}_0$ is a…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…