Related papers: The radius in matrix algebras--Examples and remark…
Let $H$ be the quantum double of a Nichols algebra of diagonal type. We compute the $R$-matrix of 3-uples of modules for general finite-dimensional highest weight modules over $H$. We calculate also a multiplicative formula for the…
The problem of computation of the joint (generalized) spectral radius of matrix sets has been discussed in a number of publications. In the paper an iteration procedure is considered that allows to build numerically Barabanov norms for the…
The quantum description of an atom with a magnetic quadrupole moment in the presence of a uniform effective magnetic field is analysed. The atom is also subject to rotation and a scalar potential proportional to the inverse of the radial…
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
We study nonmatrix varieties of $\mathbf{k}$-algebras, where $\mathbf{k}$ is a unital commutative ring. Our results extend to this generality known results for the case in which $\mathbf{k}$ is an infinite field. Also, we generalize these…
We investigate the manifold $\cal{M}$ of (real) quadratic forms in n > 1 variables having a multiple eigenvalue. In addition to known facts, we prove that 1) $\cal{M}$ is irreducible, 2) in the case of n = 3, scalar matrices and only them…
This article presents and compares four approaches for computing the rotation of a point about an axis by an angle in $\mathbb{R}^3$. We illustrate these methods by computing, by hand, the rotation of point $P=(1,0,1)^T$ about axis…
Let $\mathbb F_q$ denote the finite field with $q$ elements. In this paper we use the relationship between suitable polynomials and number of rational points on algebraic curves to give the exact number of elements $a\in \mathbb F_q$ for…
In a previous work \cite{mbeleka}, we have modelled the rotation curves (RC) of spiral galaxies by including in the equation of motion dynamical terms from an external real self-interacting scalar field, $\phi$, minimally coupled to gravity…
In this paper, we describe an elementary method for counting the number of non-isomorphic algebras of a fixed dimension over a given finite field. We show how this method works for the explicit example of $2$-dimensional algebras over the…
We present the following result: consider the space of complex polynomials of degree n>2 with n-1 distinct marked periodic orbits of given periods. Then this space is irreducible and the multipliers of the marked periodic orbits considered…
We study the maximal multiplicity locus of a variety $X$ over a field of characteristic $p>0$ that is provided with a finite surjective radical morphism $\delta:X\rightarrow V$, where $V$ is regular, for example, when…
It has been recently shown that $|| F_n(A) ||\leq 2$, where $A$ is a linear continuous operator acting in a Hilbert space, and $F_n$ is the Faber polynomial of degree $n$ corresponding to some convex compact $E\subset \mathbb C$ containing…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…
We study automorphism groups of formal matrix algebras. We also consider automorphisms of ordinary matrix algebras (in particular, triangular matrix algebras).
The geometry of algebraic curves over finite fields is a rich area of research. In previous work, the authors investigated a particular aspect of the geometry over finite fields of the classical unit circle, namely how the number of…
An $F$-algebra $A$ with unit $1$ is said to be a locally matrix algebra if an arbitrary finite collection of elements $a_1,$ $\ldots,$ $a_s $ from $ A$ lies in a subalgebra $B$ with $1$ of the algebra $A$, that is isomorphic to a matrix…
Theory of representations of F-algebra is a natural development of the theory of F-algebra. Exploring of morphisms of the representation leads to the concepts of generating set and basis of representation. In the book I considered the…
We deal with the existing problem of filtered multiplicative bases of finite-dimensional associative algebras. For an associative algebra A over a field, we investigate when the property of having a filtered multiplicative basis is…
We study the complexity of multiplication of two elements in a finite field extension given by their coordinates in a normal basis. We show how to control this complexity using the arithmetic and geometry of algebraic curves.