Related papers: Algebras and groups defined by permutation relatio…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},\ldots , a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}\cdots a_{n} =a_{\sigma (1)} a_{\sigma (2)} \cdots a_{\sigma (n)}$, where…

The class of finitely presented algebras over a field K with a set of generators a_1,...,a_n and defined by homogeneous relations of the form a_1a_2...a_n = a_{sigma(1)}a_{sigma(2)}...a_{sigma(n)}, where sigma runs through an abelian…

The class of finitely presented algebras A over a field K with a set of generators x_{1},...,x_{n} and defined by homogeneous relations of the form x_{i_1}x_{i_2}...x_{i_l}=x_{sigma(i_1)}x_{sigma(i_2)}...x_{sigma(i_l)}, where l geq 2 is a…

Let $H$ be a subgroup of $\text{Sym}_n$, the symmetric group of degree $n$. For a fixed integer $l \geq 2$, the group $G$ presented with generators $x_1, x_2, \ldots ,x_n$ and with relations $x_{i_1}x_{i_2}\cdots x_{i_l} =x_{\sigma (i_1)}…

Let A be a finitely generated commutative algebra over a field K with a presentation A=K < X_{1}, ..., X_{n} | R >, where R is a set of monomial relations in the generators X_{1}, ..., X_{n}. So A = K[S], the semigroup algebra of the monoid…

We consider algebras over a field K defined by a presentation K <x_1,..., x_n : R >, where $R$ consists of n choose 2 square-free relations of the form x_i x_j = x_k x_l with every monomial x_i x_j, i different from j, appearing in one of…

Constructions are given of Noetherian maximal orders that are finitely presented algebras over a field K, defined by monomial relations. In order to do this, it is shown that the underlying homogeneous information determines the algebraic…

In this note, we investigate how different fundamental groups of presentations of a fixed algebra $A$ can be. For finitely many finitely presented groups $G_i$, we construct an algebra $A$ such that all $G_i$ appear as fundamental groups of…

We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zero-divisor of the algebra. We proceed to make a conjecture which…

We define the completion of an associative algebra $A$ in a set $M=\{M_1,\dots,M_r\}$ of $r$ right $A$-modules in such a way that if $\mathfrak a\subseteq A$ is an ideal in a commutative ring $A$ the completion $A$ in the (right) module…

Let X be a finite set and let k be a commutative ring. We consider the k-algebra of the monoid of all relations on X, modulo the ideal generated by the relations factorizing through a set of cardinality strictly smaller than Card(X), called…

We classify finite groups $G$, such that the group algebra, $\mathbb{Q}G$ (over the field of rational numbers $\mathbb{Q}$), is the direct product of the group algebra $\mathbb{Q}[G/N]$ of a proper factor group $G/N$, and some division…

Let $A$ be an algebra over a field $K$ of characteristic zero, let $\d_1, >..., \d_s\in \Der_K(A)$ be {\em commuting locally nilpotent} $K$-derivations such that $\d_i(x_j)=\d_{ij}$, the Kronecker delta, for some elements $x_1,..., x_s\in…

Given any finitely presented group G we find a triangular algebra such that has two presentations, one with fundamental group G and another with trivial group. Thus proving that given a collection G1,...,Gn of finitely presented groups…

In this article we define $G$-algebras, that is, graded algebras on which a reductive group $G$ acts as gradation preserving automorphisms. Starting from a finite dimensional $G$-module $V$ and the polynomial ring $\mathbb{C}[V]$, it is…

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 describe a set of defining relations for automorphism groups of finitely generated free algebras of Nielsen-Schreier varieties. In particular, this gives a representation of the automorphism groups of free Lie algebras by generators and…

Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…

A classical theorem of R. Baer describes the nilpotent radical of a finite group G as the set of all Engel elements, i.e. elements y in G such that for any x in G the n-th commutator [x,y,...,y] equals 1 for n big enough. We obtain a…