Related papers: Some trace formulae involving the split sequences …

A recurrence relation is said to have the Laurent property if all of its iterates are Laurent polynomials in the initial values with integer coefficients. We consider a family of nonlinear recurrences with the Laurent property, which were…

It is shown that traces of mapping classes of finite order may be expressed by Verlinde-like formulae. The 3D topological argument is explained, and the resulting trace identities for modular matrix elements are presented.

In this paper we define two Lie operations, and with that we define the bicharacter algebras, Nichols bicharacter algebras, quantum Nichols bicharacter algebras, etc. We obtain explicit bases for $\mathfrak L(V)${\tiny $_{R}$} and…

We study tridiagonal pairs of type II. These involve two linear transformations $A$ and $A^\star$. We define two bases. In the first one, $A$ acts as a diagonal matrix while $A^\star$ acts as a block tridiagonal matrix, and in the second…

The aim of this article is twofold: give a short proof of the existence of real spectral shift function and the associated trace formula for a pair of contractions, the difference of which is trace-class and one of the two a strict…

Let $\mathbb{K}$ denote a field and let $\mathfrak{X}$ denote a finite non-empty set. Let $\text{Mat}_\mathfrak{X}(\mathbb{K})$ denote the $\mathbb{K}$-algebra consisting of the matrices with entries in $\mathbb{K}$ and rows and columns…

A subset X of a vector space V is said to have the "Separation Property" if it separates linear forms in the following sense: given a pair (a, b) of linearly independent forms on V there is a point x on X such that a(x)=0 and b(x) is not…

We consider a family of nonlinear recurrences with the Laurent property. Although these recurrences are not generated by mutations in a cluster algebra, they fit within the broader framework of Laurent phenomenon algebras, as introduced…

Let $V$ be the set of $n\times n$ complex or real general matrices, Hermitian matrices, symmetric matrices, positive definite (resp. semi-definite) matrices, diagonal matrices, or upper triangular matrices. Fix $k\in \mathbb{Z}\setminus…

This paper considers computational methods that split a vector field into three components in the case when both the vector field and the split components might be unbounded. We first employ classical Taylor expansion which, after some…

We introduce a linear algebraic object called a bidiagonal triple. A bidiagonal triple consists of three diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the…

Sequence transformations are important tools for the convergence acceleration of slowly convergent scalar sequences or series and for the summation of divergent series. Transformations that depend not only on the sequence elements or…

This paper deals with the following problem. Given a finite extension of fields $\mathbb{L}/\mathbb{K}$ and denoting the trace map from $\mathbb{L}$ to $\mathbb{K}$ by $\mathrm{Tr}$, for which elements $z$ in $\mathbb{L}$, and $a$, $b$ in…

We give a canonical form of matrices of a cycle of linear or semilinear mapping V_1 --- V_2 --- ... --- V_t --- V_1 in which all V_i are complex vector spaces, each line is an arrow ---> or <---, and each arrow denotes a linear or…

Let $\boldsymbol{\Lambda}\,(=\mathbb{F}^{n^{3}})$, where $\mathbb{F}$ is a field with $|\mathbb{F}|>2$, be the space of structure vectors of algebras having the $n$-dimensional $\mathbb{F}$-space $V$ as the underlying vector space. Also let…

Motivated by the study of traces on graph $C^*$-algebras, we consider traces (additive, central maps) on Leavitt path algebras, the algebraic counterparts of graph $C^*$-algebras. In particular, we consider traces which vanish on nonzero…

Let $M$ be a closed orientable Riemannian surface. Consider an SO(3)-connection $A$ and a Higgs field $\Phi:M\to so(3)$. The pair $(A,\Phi)$ naturally induces a cocycle over the geodesic flow of $M$. We classify (up to gauge…

Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…

In this paper we use topological techniques to construct generalized trace and modified dimension functions on ideals in certain ribbon categories. Examples of such ribbon categories naturally arise in representation theory where the usual…

We study trace functions on the form $ t\to\tr f(A+tB) $ where $ f $ is a real function defined on the positive half-line, and $ A $ and $ B $ are matrices such that $ A $ is positive definite and $ B $ is positive semi-definite. If $ f $…