Related papers: The unbroken spectra of Frobenius seaweeds

In this work we introduce the notion of almost-symmetry for generalized numerical semigroups. In addition to the main properties occurring in this new class, we present several characterizations for its elements. In particular we show that…

We investigate the properties of principal elements of Frobenius Lie algebras, following the work of M. Gerstenhaber and A. Giaquinto. We prove that any Lie algebra with a left symmetric algebra structure can be embedded, in a natural way,…

For a graph $G$, the spectral radius of $G$ is the largest eigenvalue of its adjacency matrix. A connected factor of $G$ is a connected spanning subgraph of $G$. For example, a spanning tree of $G$ is a 1-connected factor of $G$. Let $G$ be…

We consider an integrable system in five unknowns having three quartics invariants. We show that the complex affine variety defined by putting these invariants equal to generic constants, completes into an abelian surface; the jacobian of a…

We investigate the peripheral spectrum of irreducible positive elements of an ordered Banach algebra. In particular, we give conditions under which the peripheral spectrum contains (or coincides with) the cyclic group generated by a root of…

We give formulas for the multiplicity of any affine isolated zero of a generic polynomial system of n equations in n unknowns with prescribed sets of monomials. First, we consider sets of supports such that the origin is an isolated root of…

Let $\mathcal{R} = \mathbb{K}[x_1, \dots, x_n]$ be a multivariate polynomial ring over a field $\mathbb{K}$ of characteristic 0. Consider $n$ algebraically independent elements $g_1, \dots, g_n$ in $\mathcal{R}$. Let $\mathcal{S}$ denote…

Given an exact functor between triangulated categories which admits both adjoints and whose cotwist is either zero or an autoequivalence, we show how to associate a unique full triangulated subcategory of the codomain on which the functor…

We introduce a family of posets which generate Lie poset subalgebras of $A_{n-1}=\mathfrak{sl}(n)$ whose index can be realized topologically. In particular, if $\mathcal{P}$ is such a \textit{toral poset}, then it has a simplicial…

We find the spectrum and eigenvectors of an arbitrary irreducible complex tridiagonal matrix with two-periodic main diagonal provided that the spectrum and eigenvectors of the matrix with the same sub- and superdiagonals and zero main…

Using a suitable notion of principal G-bundle, defined relative to an arbitrary cartesian category, it is shown that principal bundles can be characterised as adjunctions that stably satisfy Frobenius reciprocity. The result extends from G,…

We characterize possible spectra of rank-one perturbations B of a self-adjoint operator A with discrete spectrum and, in particular, prove that the spectrum of B may include any number of real or non-real eigenvalues of arbitrary algebraic…

We present a unified apoach to the study of separable and Frobenius algebras. The crucial observation is thsat both cases are related to the nonlinear equation $R^{12}R^{23}=R^{23}R^{13}=R^{13}R^{12}$, called the FS-equation. Given a…

We study the distribution of the traces of the Frobenius endomorphism of genus $g$ curves which are quartic non-cyclic covers of $\mathbb{P}^{1}_{\mathbb{F}_{q}}$, as the curve varies in an irreducible component of the moduli space. We show…

Let $T$ be a tree with an irreducible characteristic polynomial $\phi(x)$ over $\mathbb{Q}$. Let $\Delta(T)$ be the discriminant of $\phi(x)$. It is proved that if $2^{-\frac n2}\sqrt{\Delta(T)}$ (which is always an integer) is odd and…

The homogeneous spectrum of a multigraded finitely generated algebra (in the sense of Brenner-Schr\"oer) always admits an embedding into a toric variety that is not necessarily separated, a so-called toric prevariety. In order to have a…

Consider the jacobian of a hyperelliptic genus two curve defined over a finite field. Under certain restrictions on the endomorphism ring of the jacobian we give an explicit description all non-degenerate, bilinear, anti-symmetric and…

For a hypersurface isolated singularity defined by a convergent power series $f$, the Steenbrink spectrum can be defined as the Poincar\'e polynomial of the graded quotients of the $V$-filtration on the Jacobian ring of $f$. The Tjurina…

Let $A=(a_1, a_2, \ldots, a_n)$ be a sequence of relative prime positive integers with $a_i\geq 2$. The Frobenius number $F(A)$ is the largest integer not belonging to the numerical semigroup $\langle A\rangle$ generated by $A$. The genus…

We characterize Frobenius and separable monoidal algebra extensions $i: R\ra S$ in terms given by $R$ and $S$. For instance, under some conditions, we show that the extension is Frobenius, respectively separable, if and only if $S$ is a…