Related papers: Central polynomials with involution for the algebr…

In this paper we describe graded automorphisms and antiautomorphisms of finite order on matrix algebras endowed with a group gradings by a finite abelian group over an arbitrary algebraically closed field of charcteristic different from 2.

Up to linear transformations, we obtain a classification of permutation polynomials (PPs) of degree $8$ over $\mathbb{F}_{2^r}$ with $r>3$. By [J. Number Theory 176 (2017) 466-66], a polynomial $f$ of degree $8$ over $\mathbb{F}_{2^r}$ is…

We consider the problem of characterizing upper-triangular matrices $M=\begin{pmatrix}p&r\\0&q\end{pmatrix}\in M_2(\mathbb Z)$ which can be represented in the form $A^2-B^2$ with upper-triangular integer matrices $A$ and $B$ and give a…

Let $FG$ be the group algebra of a finite $2$-group $G$ over a finite field $F$ of characteristic two and $\circledast$ an involution which arises from $G$. The $\circledast$-unitary subgroup of $FG$, denoted by $V_{\circledast}(FG)$, is…

Let F be a field with characteristic two. We generalize the second trace form for central simple algebras with odd degree over F. We determine the second trace form and the Arf invariant and Clifford invariant for tensor products of central…

In this paper, we introduce the degenerate central factorial polynomials and numbers of the second kind which are degenerate versions of the central factorial polynomials and numbers of the second kind. We derive some properties and…

We study the duality between the mutations and the initial-seed mutations in cluster algebras, where the initial-seed mutations are the transformations of rational expressions of cluster variables in terms of the initial cluster under the…

We study totally decomposable symplectic and unitary involutions on central simple algebras of index 2 and on split central simple algebras respectively. We show that for every field extension, these involutions are either anisotropic or…

Let $F$ be an infinite field and $UT(d_1,\dots, d_n)$ be the algebra of upper block-triangular matrices over $F$. In this paper we describe a basis for the $G$-graded polynomial identities of $UT(d_1,\dots, d_n)$, with an elementary grading…

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…

Let $N_n(F)$ denote the ring of strictly upper triangular matrices with entries in a field $F$ of characteristic zero and center $Z(N_n(F))$. We characterize the $2$-power commuting maps over $N_n(F)$, maps satisfying the identity…

Let L be a restricted Lie superalgebra with its restricted enveloping algebra u(L) over a field F of characteristic p>2. A polynomial identity is called non-matrix if it is not satisfied by the algebra of 2\times 2 matrices over F. We…

Permutation polynomials over finite fields have wide applications in many areas of science and engineering. In this paper, we present six new classes of permutation trinomials over $\mathbb{F}_{2^n}$ which have explicit forms by determining…

An important invariant of a polynomial $f$ is its Jacobian algebra defined by its partial derivatives. Let $f$ be invariant with respect to the action of a finite group of diagonal symmetries $G$. We axiomatically define an orbifold…

For any polynomial $P \in \mathbb{C}[X_1,X_2,...,X_n]$, we describe a $\mathbb{C}$-vector space $F(P)$ of solutions of a linear system of equations coming from some algebraic partial differential equations such that the dimension of $F(P)$…

Let E be the infinite dimensional Grassmann algebra over a field F of characteristic 0. In this paper we compute the ordinary and the Z/2Z-graded cocharacters of the algebra of 2x2 upper triangular matrices with coefficients in E, using the…

For all finite fields of $q$ elements where $q\equiv1\pmod4$ we have constructed permutation polynomials which have order 2 as permutations, and have 3 terms, or 4 terms as polynomials. Explicit formulas for their coefficients are given in…

In this paper, we investigate subnormal subgroups of the multiplicative group of an almost locally simple artinian algebra with involution. In particular, we show that if either the set of traces or the set of norms of such a subgroup with…

We propose an explicit representation of central $(2k+1)$-nomial coefficients in terms of finite sums over trigonometric constructs. The approach utilizes the diagonalization of circulant boolean matrices and is generalizable to all…

We generalize the solution of linear recurrence relations from fields to central division algebras, adapting the standard tools of companion matrices and characteristic polynomials to the non-commutative setting. We then solve linear…