Related papers: The Ends of Algebras
We explicate a number of notions of algebraic laminations existing in the literature, particularly in the context of an exact sequence $$1\to H\to G \to Q \to 1 $$ of hyperbolic groups. These laminations arise in different contexts:…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
We study completions of the group algebra of a finitely generated group and relate nuclearity of such a completion to growth properties of the group. This extends previous work of Jolissaint on nuclearity of rapidly decreasing functions on…
In this note, we observe a relation between dialgebras (in particular, Leibniz algebras) and conformal algebras. The purpose is to show how the methods of conformal algebras help solving problems on dialgebras, and, conversely, how the…
We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.
We obtain a lifting property for finite quotients of algebraic groups, and applications to the structure of these groups.
These notes briefly discuss finite-dimensional algebras with involutions, self-adjoint elements, and so on.
We give a presentation of a finite crystallographic reflection group in terms of an arbitrary seed in the corresponding cluster algebra of finite type and interpret the presentation in terms of companion bases in the associated root system.
The aim of this paper is to unify the points of view of three recent and independent papers (Ventura 1997, Margolis, Sapir and Weil 2001 and Kapovich and Miasnikov 2002), where similar modern versions of a 1951 theorem of Takahasi were…
Motivated by the theory of graph limits, we introduce and study the convergence and limits of linear representations of finite groups over finite fields. The limit objects are infinite dimensional representations of free groups in…
We deal with equations over free semilattice of infinite rank and prove that any infinite consistent system of equations is equivalent to its finite subsystem. Moreover, we describe irreducible algebraic sets and solve some algorithmic…
We introduce the notion of a genus and its mass for vertex algebras. For lattice vertex algebras, their genera are the same as those of lattices, which plays an important role in the classification of lattices. We derive a formula relating…
In this paper we try to define the higher dimensional analogues of vertex algebras. In other words we define algebras which we hope have the same relation to higher dimensional quantum field theories that vertex algebras have to one…
Making a survey of recent constructions of universal cohomologies we suggest a new framework for a theory of motives in algebraic geometry.
For the first time, we have introduced the concept of N-groups, N-semigroups, N-loops, and N-groupoids. We also define a mixed N-algebraic structure. The main aim of this book is to attract young mathematicians to this interesting field. It…
We introduce decomposition algebras as a natural generalization of axial algebras, Majorana algebras and the Griess algebra. They remedy three limitations of axial algebras: (1) They separate fusion laws from specific values in a field,…
We view difference algebra as the study of algebraic objects in the topos of difference sets. The methods of topos theory and categorical logic enable us to develop difference homological algebra, identify a solid foundation for difference…
For a class of nonassociative metagroup algebras their separability is investigated. For this purpose the cohomology theory on them is utilized. Conditions are found under which nonassociative metagroup algebras are separable. Algebras…
We give an overview of differential cohomology from the point of view of algebraic topology. This includes a survey of several different definitions of differential cohomology groups, a discussion of differential characteristic classes, an…
Computations in the cohomology of finite groups.