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In characteristic two, it is shown that a central simple algebra of degree equal to a power of two with anisotropic orthogonal involution is totally decomposable, if it becomes either anisotropic or metabolic over all extensions of the…

A loop whose inner mappings are automorphisms is an \emph{automorphic loop} (or \emph{A-loop}). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the isomorphism problem. Using this characterization and certain…

In this paper, by using the theory of circulant matrices we study some matrices over finite fields which involve the quadratic character and trinomial coefficients.

We classify three dimensional evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.

We show how to define, for every Riordan group element $(g(x), f(x))$, an involution in the Riordan group. More generally, we show that for every pseudo-involution $P$ in the Riordan group, we can define a new involution beginning with an…

The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in…

In this paper we introduce a method of characteristic sets with respect to several term orderings for difference-differential polynomials. Using this technique, we obtain a method of computation of multivariate dimension polynomials of…

The question of whether a split tensor product of quaternion algebras with involution over a field of characteristic two can be expressed as a tensor product of split quaternion algebras with involution, is shown to have an affirmative…

Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi--orthogonality conditions. We obtain several characterizations for these…

We define a family of polynomial ring homomorphisms generalizing the well-known Nagata automorphism. We establish necessary and sufficient conditions under which these homomorphisms are automorphisms, and verify that they satisfy the…

We develop a theory of loops with involution. On this basis we define a Cayley-Dickson doubling on loops, and use it to investigate the lattice of varieties of loops with involution, focusing on properties that remain valid in the…

We give a general multiplication-convolution identity for the multivariate and bivariate rank generating polynomial of a matroid. The bivariate rank generating polynomial is transformable to and from the Tutte polynomial by simple algebraic…

We investigate the second-order correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for the generating function, we re-obtain several well-known kernels from random matrix…

Let $K$ be an algebraically closed field of characteristic zero, and let $A$ and $B$ be two simple algebras with involution over $K$. In this note we study the embedding problem for algebras with involution. More specifically, if the…

An important aspect in the theory of algebras with polynomial identities is the study of the asymptotic behavior of the codimension sequence $c_n(A),\, n\geq 1,$ which measures the growth of polynomial identities of a given algebra $A$. In…

We study the differential polynomial rings which are defined using the special geometry of the moduli spaces of Calabi-Yau threefolds. The higher genus topological string amplitudes are expressed as polynomials in the generators of these…

We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…

In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…

An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such…

The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of…