Related papers: The PI Property in Algebras of Polynomial Type
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…
We find a class of algebras A satisfying the following property: for every nontrivial noncommutative polynomial, the linear span of all its values in A equals A. This class includes the algebras of all bounded and all compact operators on…
We define the notion of an almost polynomial identity of an associative algebra $R$, and show that its existence implies the existence of an actual polynomial identity of $R$. A similar result is also obtained for Lie algebras and Jordan…
In this article, we give an account of some recent irreducibility testing criteria for polynomials having integer coefficients over the field of rational numbers.
We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (noncommutative differential geometry, noncommutative algebraic…
This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.
Numerical characteristics of polynomial identities of left nilpotent algebras are examined. Previously, we came up with a construction which, given an infinite binary word, allowed us to build a two-step left nilpotent algebra with…
In this article we shows some results about algebra with the group of units having special polynomial identity.
We study polynomial identities of algebras with involution of nonassociative algebras over a field of characteristic zero. We prove that the growth of the sequence of $*$-codimensions of a finite-dimensional algebra is exponentially…
Numerical characteristics of identities of finite-dimensional nonassociative algebras are studied. The main result is the construction of a four-dimensional simple unitary algebra with fractional PI-exponent strictly less than its…
This article discuss a class of tractable model in the form of polynomial type.
This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra.
We investigate algebraic and arithmetic properties of a class of sequences of sparse polynomials that have binomial coefficients both as exponents and as coefficients. In addition to divisibility and irreducibility results we also consider…
We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field by using the braiding structures of A. We investigate basic properties of the polynomial invariants including stability…
We study polynomial identities of algebras with adjoined external unit. For a wide class of algebras we prove that adjoining external unit element leads to increasing of PI-exponent precisely to 1. We also show that any real number from the…
This paper gives an overview of some basic properties of Leibniz algebras. Some of the results were known earlier, but in the article they are accompanied by new simple proofs. Some of the results are new. The article can be viewed as a…
We study identities of finite dimensional algebras over a field of characteristic zero, graded by an arbitrary groupoid $\Gamma$. First we prove that its graded colength has a polynomially bounded growth. For any graded simple algebra $A$…
In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties,…
We compute the PI-exponent of the matrix ring with coefficients in an associative algebra. As a consequence, we prove the following. Let $\mathcal{R}$ be a PI-algebra with a positive PI-exponent. If $M_n(\mathcal{R})$ and $M_m(\mathcal{R})$…
This is a survey of some recent developments concerning the p-adic cohomology of algebraic varieties over fields of positive characteristic and local fields of mixed characteristic, plus some related areas like p-adic Hodge theory.