Related papers: The geometry of polynomial identities

This paper studies geometric properties of the Iterated Matrix Multiplication polynomial and the hypersurface that it defines. We focus on geometric aspects that may be relevant for complexity theory such as the symmetry group of the…

In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.

In this paper we introduce the concept of polynomial diagrams and its area for special polynomials.We study the properties of polynomial area diagrams. The formula for the area of an arbitrary polynomial diagram.

We study and derive identities for the multi-variate independence polynomials from the perspective of heaps theory. Using the inversion formula and the combinatorics of partially commutative algebras we show how the multi-variate version of…

We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.

Let $F$ be a field of characteristic zero and $W$ be an associative affine $F$-algebra satisfying a polynomial identity (PI). The codimension sequence associated to $W$, $c_n(W)$, is known to be of the form $\Theta (c n^t d^n)$, where $d$…

We consider associative algebras over a field of characteristic zero. We give a version of the proof of the Kemer's theorems concerning the Specht problem solution. It is proved that the ideal of graded identities of a finitely generated…

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 article we shows some results about algebra with the group of units having special polynomial identity.

In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.

In this paper, we study some properties of Euler polynomials arising from umbral calculus. Finally, we give some interesting identities of Euler polynomials using our results. Recently, Dere and Simsek have studied umbral calculus related…

In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials

In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the…

The aim of this study is to show that harmonic geometric polynomials can be represented in terms of geometric polynomials. This problem was first considered by Keller [14]; however, the corresponding coefficients were not fully determined.…

Let $A$ be an associative algebra over a field $F$ of characteristic zero and let $L$ be a Lie algebra over $F$. If $L$ acts on $A$ by derivations, then such an action determines an action of its universal enveloping algebra $U(L)$ and in…

In this paper, we investigate some properties of q-Bernoulli polynomi- als arising from q-umbral calculus. Finally, we derive some interesting identities of q-Bernoulli polynomials from our investigation.

We study a class of complex polynomial equations on a finite graph with a view to understanding how holistic phenomena emerge from combinatorial structure. Particular solutions arise from orthogonal projections of regular polytopes,…

In this work, we derive numerous identities for multivariate q-Euler polynomials by using umbral calculus.

Let D be a domain with quotient field K and A a D-algebra. We call a polynomial with coefficients in K that maps every element of A to an element of A "integer-valued on A". For commutative A we also consider integer-valued polynomials in…

This article provides a synthesis of recent advances in the study of the PI property in various classes of noncommutative algebras of polynomial type.