Related papers: Zero Divisors in Associative Algebras over Infinit…

We show that in a tracial and finitely generated $W^\ast$-probability space existence of conjugate variables excludes algebraic relations for the generators. Moreover, under the assumption of maximal non-microstates free entropy dimension,…

Each irreducible representation of the affine group of a finite field has a unique maximal inductive algebra, and it is self adjoint.

Let M be a Q-divisor on a smooth surface over C. In this paper we give criteria for very ampleness of the adjoint of the round-up of M. (Similar results for global generation were given by Ein and Lazarsfeld and used in their proof of…

The paper is devoted to the investigation of finite dimensional commutative nilpotent (associative) algebras N over an arbitrary base field of characteristic zero. Due to the lack of a general structure theory for algebras of this type (as…

The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…

We prove that the algebraic set of pairs of matrices with a diagonal commutator over a field of positive prime characteristic, its irreducible components, and their intersection are $F$-pure when the size of matrices is equal to 3.…

Let $R$ be a commutative ring with identity and let $I$ be an ideal of $R$. Let $R\Join I$ be the subring of $R\times R$ consisting of the elements $(r,r+i)$ for $r\in R$ and $i\in I$. We study the diameter and girth of the zero-divisor…

We describe the group of continuous automorphisms of all simple infinite-dimensional linearly compact Lie superalgebras and use it in order to classify F-forms of these superalgebras over any field F of characteristic zero.

For an associative algebra $A$ a skew-symmetric sum of $n!$ products of $n$ elements of $A$ in all possible order is called $n$-commutator. We consider $A$ as $n$-ary algebra under $n$-commutator. We prove that it has an identity of…

In this paper we look into the structure of finite-dimensional graded superalgebras of various types such as associative, Lie and Jordan over an algebraically closed field of characteristic zero.

In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including…

Let k be an algebraically closed field and A a finite dimensional associative k-algebra. We prove that there is no gap in the lengths of indecomposable A-modules of finite length. The analogous result holds for an abelian k-linear category…

We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…

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…

The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…

We establish many previously unknown properties of zero-divisors in Cayley-Dickson algebras. The basic approach is to use a certain splitting that simplifies computations surprisingly.

The purpose of the article is to provide an unified way to formulate zero-sum invariants. Let $G$ be a finite additive abelian group. Let $B(G)$ denote the set consisting of all nonempty zero-sum sequences over G. For $\Omega \subset B(G$),…

Let ${\bf F}$ be a field of characteristic zero. It is proved that for any finitely generated linear group $\Gamma<\mathsf{GL}_n({\bf F})$, every unipotent-free abelian subgroup of $\Gamma$ is separable.

We prove that the genus of a finite-dimensional division algebra is finite whenever the center is a finitely generated field of any characteristic. We also discuss potential applications of our method to other problems, including the…

We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre…