Related papers: Algebras and groups defined by permutation relatio…

In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form $n$ over a field $k$ of characteristic not two, and a category arising from an action…

Let $K\langle X\rangle =K\langle X_1,...,X_n\rangle$ be the free algebra of $n$ generators over a field $K$, and let $R\langle X\rangle =R\langle X_1,...,X_n\rangle$ be the free algebra of $n$ generators over an arbitrary commutative ring…

We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to the one of equational classes defined by equation arrows. Free…

An approach to representations of finite groups is presented without recourse to character theory. Considering the group algebra C[G] as an algebra of linear maps on C[G] (by left multiplication), we derive the primitive central idempotents…

In this paper we classify the isomorphism classes of four dimensional nilpotent associative algebras over a field F, studying regular subgroups of the affine group AGL_4(F). In particular we provide explicit representatives for such classes…

There has been a great deal of attention recently to graphs whose vertex set is a group, defined using the group structure. (The commuting graph, where two elements are joined if they commute, is the oldest and most famous example.) The…

We prove a general result on presentations of finitely-generated algebras and apply it to obtain nice presentations for some noncommutative algebras arising in the matrix bispectral problem. By "nice presentation" we mean a presentation…

The {\it prime graph} $\Gamma(G)$ of a finite group $G$ is the graph whose vertex set is the set of prime divisors of $|G|$ and in which two distinct vertices $r$ and $s$ are adjacent if and only if there exists an element of $G$ of order…

We develop a structure theory for nilpotent symplectic alternating algebras. We then give a classification of all nilpotent symplectic alternating algebras of dimension up to 10 over any field. The study reveals a new subclasses of powerful…

We consider algebras with basis numerated by elements of a group $G.$ We fix a function $f$ from $G\times G$ to a ground field and give a multiplication of the algebra which depends on $f$. We study the basic properties of such algebras. In…

We define a class of algebras describing links of binary semi-isolating formulas on a set of realizations for a family of 1-types of a complete theory. These algebras include algebras of isolating formulas considered before. We prove that a…

We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined…

We show that pseudovarieties of finitely generated algebras, i.e., classes $C$ of finitely generated algebras closed under finite products, homomorphic images, and subalgebras, can be described via a uniform structure $U$ on the free…

Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero…

Let W be a finite Coxeter group. We define its Hecke-group algebra by gluing together appropriately its group algebra and its 0-Hecke algebra. We describe in detail this algebra (dimension, several bases, conjectural presentation,…

We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a…

We show that group C*-algebras of finitely generated, nilpotent groups have finite nuclear dimension. It then follows, from a string of deep results, that the C*-algebra $A$ generated by an irreducible representation of such a group has…

Let A be a finite dimensional algebra over an algebraically closed field with the radical nilpotent of index 2. It is shown that A has finitely many conjugacy classes of left ideals if and only if A is of finite representation type provided…

Let k be a field of characteristic zero. We consider graded subalgebras A of k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear forms. Representations of matroids over k provide a natural description of the…

We prove that two finite-dimensional commutative algebras over an algebraically closed field are isomorphic if and only if they give rise to isomorphic representations of the category of finite sets and surjective maps.