Related papers: Choi matrices revisited. II
We investigate symmetric quotient algebras of symmetric algebras, with an emphasis on finite group algebras over a complete discrete valuation ring ${\mathcal O}$. Using elementary methods, we show that if an ordinary irreducible character…
We first present a determinant inequality related to partial traces for positive semidefinite block matrices. Our result extends a result of Lin [Czech. Math. J. 66 (2016)] and improves a result of Kuai [Linear Multilinear Algebra 66…
We construct a new class of positive indecomposable maps in the algebra of 'd x d' complex matrices. Each map is uniquely characterized by a cyclic bistochastic matrix. This class generalizes a Choi map for d=3. It provides a new reach…
Let $A$, $B$ be multidimensional matrices of boundary format respectively $\prod_{i=0}^p(k_i+1)$, $\prod_{j=0}^q(l_j+1)$. Assume that $k_p=l_0$ so that the convolution $A\ast B$ is defined. We prove that $Det (A\ast B)=Det(A)^{\alpha}\cdot…
The inverses of indecomposable Cartan matrices are computed for finite-dimensional Lie algebras and Lie superalgebras over fields of any characteristic, and for hyperbolic (almost affine) complex Lie (super)algebras. We discovered three yet…
We extend the Galilei group of space-time transformations by gradation, construct interacting field-theoretic representations of this algebra, and show that non-relativistic Super-Chern-Simons theory is a special case. We also study the…
Bochner's theorem characterizes positive definite functions on groups through the positivity of their Fourier transforms and plays a fundamental role in Harmonic analysis. While Bochner-type results are known for certain classes of…
The paper discusses four approaches to the biextension of Chow groups and their equivalences. These are the following: an explicit construction given by S.Bloch, a construction in terms of the Poincare biextension of dual intermediate…
A linear map $\Phi$ between matrix spaces is called cross-positive if it is positive on orthogonal pairs $(U,V)$ of positive semidefinite matrices in the sense that $\langle U,V\rangle:=\text{Tr}(UV)=0$ implies $\langle…
Let $V$ be a vector space of rectangular $n\times k$ matrices annihilating the Cullis' determinant. We show that $\dim(V) \le (n-1)k$, extending Dieudonn{\'{e}}'s result on the dimension of vector spaces of square matrices annihilating the…
Let $G_1, \dots, G_k$ be finite-dimensional vector spaces over a finite field $\mathbb{F}$. A multilinear variety of codimension $d$ is a subset of $G_1 \times \dots \times G_k$ defined as the zero set of $d$ forms, each of which is…
In this paper we consider the decomposition of positive semidefinite matrices as a sum of rank one matrices. We introduce and investigate the properties of various measures of optimality of such decompositions. For some classes of positive…
In this paper, we prove the positivity of the double mixed discriminant associated with a positive linear map between spaces of third-order complex matrices, thereby settling the three-dimensional case of Finski's open problem. As an…
Monodromy matrices of the $\tau_2$ model are known to satisfy a Yang--Baxter equation with a six-vertex $R$-matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this…
The main goal of the paper is the discussion of a deeper interaction between matrix theory over polynomial rings over a field and typical methods of commutative algebra and related algebraic geometry. This is intended in the sense of…
We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…
A reciprocal linear space is the image of a linear space under coordinate-wise inversion. These fundamental varieties describe the analytic centers of hyperplane arrangements and appear as part of the defining equations of the central path…
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 study positive bilinear forms on a Hilbert space which are neither not necessarily bounded nor induced by some positive operator. We show when different families of bilinear forms can be described as a generalized effect algebra. In…
Positive maps that are not decomposable are a key resource in entanglement theory because they can detect bound entangled states, yet systematic methods for constructing them remain limited. We introduce an optimization framework based on…