Related papers: A constructive proof of Pokrzywa's theorem about p…

In this paper we prove the Jordan-Kronecker theorem which gives a canonical form for a pair of skew-symmetric bilinear forms on a finite-dimensional vector space over an algebraically closed field.

In this paper we prove a conjecture regarding the form of the Born-Infeld Lagrangian with a U(1)^2n gauge group after the elimination of the auxiliary fields. We show that the Lagrangian can be written as a symmetrized trace of Lorentz…

We present a new solution to the classification problem for the category of representations of a quiver of type $\widetilde{A}_{3}$. Our approach uses linear algebra techniques which lead us to a reduction that allows to use induction. As…

This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $\alpha$, and $\nu$. The time-independent Schr\"{o}dinger equation for the induced deformed harmonic oscillator is solved; explicit analytic…

Matrix polynomials given in an orthogonal basis are considered. Following the ideas of Mackey et al. "Vector spaces of Linearizations for Matrix Polynomials" (2006), the vec- tor spaces, called M1(P), M2(P) and DM(P), of potential…

We consider a quadratic matrix boundary value problem with equations and boundary conditions dependent on a spectral parameter. We study an inverse problem that consists in recovering the differential pencil by the so-called Weyl matrix. We…

The strong spectral order induces a natural partial ordering on the manifold $H_{n}$ of monic hyperbolic polynomials of degree $n$. We prove that twisted root maps associated with linear operators acting on $H_{n}$ are G\aa rding convex on…

We obtain a presentation by generators and relations of any Nichols algebra of diagonal type with finite root system. We prove that the defining ideal is finitely generated. The proof is based in Kharchenko's theory of PBW basis of Lyndon…

In recent years, various nonlinear algebraic structures have been obtained in the context of quantum systems as symmetry algebras, Painlev\'{e} transcendent models and missing label problems. In this paper we treat all of these algebras as…

In this paper, we introduce a class of infinite matrices related to the Beurling algebra of periodic functions, and we show that it is an inverse-closed subalgebra of ${\mathcal B}(\ell^q_w)$, the algebra of all bounded linear operators on…

We refine the invariant on $K_2(A[C_{p_e}]/I_m,(T-1))$ constructed in a previous paper to one which is an isomorphism for all $\lambda$-rings $A$.

We present Lie-algebraic deformations of Minkowski space with undeformed Poincar\'{e} algebra. These deformations interpolate between Snyder and $\kappa$-Minkowski space. We find realizations of noncommutative coordinates in terms of…

Analytical tools to $K$-theory; namely, self-stabilization of rapidly decreasing matrices, linearization of cyclic loops, and the contractibility of the pointed stable Toeplitz algebra are discussed in terms of concrete formulas. Adaptation…

First-order perturbative calculation of the frequency-shifts caused by special relativity is performed for a charged particle confined in a Penning trap. The perturbed motion is approximated by the Jacobian elliptic functions which describe…

Let $A_1, \ldots, A_r$ be Hermitian $n \times n$ matrices and $S = \sum A_i \otimes s_i$ the associated matrix semicircle, where $s_1, \ldots, s_r$ are free semicircular variables. We prove that the following are equivalent: (i) the matrix…

For any pencil of conics or higher-dimensional quadrics over the rationals, with all degenerate fibres defined over the rationals, we show that the Brauer-Manin obstruction controls weak approximation. The proof is based on the Hasse…

In this paper we study the problem of classifying pencils of curves of degree $d$ in $\mathbb{P}^2$ using geometric invariant theory. We consider the action of $SL(3)$ and we relate the stability of a pencil to the stability of its…

We give canonical matrices of a pair (A,B) consisting of a nondegenerate form B and a linear operator A satisfying B(Ax,Ay)=B(x,y) on a vector space over F in the following cases: (i) F is an algebraically closed field of characteristic…

Let $\lambda$ and $\kappa$ be cardinal numbers such that $\kappa$ is infinite and either $2\leq \lambda\leq \kappa$, or $\lambda=2^\kappa$. We prove that there exists a lattice $L$ with exactly $\lambda$ many congruences, $2^\kappa$ many…

We study polynomial SL-invariants of tensors, mainly focusing on fundamental invariants which are of smallest degrees. In particular, we prove that certain 3-dimensional analogue of the Alon--Tarsi conjecture on Latin cubes considered…