Related papers: Some additive decompositions of $\mathbb{K}$-regul…
In this note, we initiate a study of the finite-dimensional representation theory of a class of algebras that correspond to noncommutative deformations of compact surfaces of arbitrary genus. Low dimensional representations are investigated…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
We use representation theory to construct spaces of matrices of constant rank. These spaces are parametrized by the natural representation of the general linear group or the symplectic group. We present variants of this idea, with more…
We review some recent results on $K$-theory of perfection of commutative $\mF_p$-algebras and provide an alternative proof.
We give several unequivalent notions of convergency of meromorphic functions and more generally meromorphic mappings (strong, weak, $\Gamma $-convergency and some others). Relations between them are investigated. A version of Rouche theorem…
V.I. Arnold [Russian Math. Surveys 26 (2) (1971) 29-43] constructed a miniversal deformation of matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced…
We classify the matrices M which correspond to finite categories
The symmetry properties of the dynamical matrix are well described in multiple classic textbooks. This short paper revisits the issue to demonstrate alternative form of dynamical matrix which explicitly shows its symmetry and reality in…
In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…
We extend the theory of equitable decompositions, in which, if a graph has a particular type of symmetry, i.e. a uniform or basic automorphism $\phi$, it is possible to use $\phi$ to decompose a matrix $M$ appropriately associated with the…
We construct a notion of derived completion which applies to homomorphisms of commutative S-algebras. We study the relationship of the construction with other constructions of completions, and prove various invariance properties. The…
Some properties of the multiway discrepanc of rectangular matrices of nonnegative entries are discussed. We are able to prove the continuity of this discrepancy, as well as some statements about the multiway discrepancy of some special…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…
We study k Kadison Schwarz (k KS) mappings on matrix algebras and derive explicit conditions ensuring the k KS property for two classes of maps parameterized by a single k-positive map.
A unimodular complex surface is a complex 2-manifold X endowed with a holomorphic volume form. A strictly pseudoconvex real hypersurface M in X inherits not only a CR-structure but a canonical coframing as well. In this article, this…
We describe additive surjections on direct sum of matrix algebras that preserve singularity in one direction. As an application, we classify additive surjections on finite-dimensional $C^\ast$-algebras that preserve mutual strong…
We classify all decompositions of $M_3(\mathbb{C})$ into a direct vector-space sum of two subalgebras such that one of the subalgebras contains the identity matrix.
For arbitrary F-algebra, in which the operation of addition is defined, I explore biring of matrices of mappings. The sum of matrices is determined by the sum in F-algebra, and the product of matrices is determined by the product of…
We expose different methods of regularizations of subsolutions in the context of discrete weak KAM theory. They allow to prove the existence and the density of $C^{1,1}$ subsolutions. Moreover, these subsolutions can be made strict and…