Related papers: A survey on algebraic dilatations
A general deformation theory of algebras which factorise into two subalgebras is studied. It is shown that the classification of deformations is related to the cohomology of a certain double complex reminiscent of the Gerstenhaber-Schack…
A dilatation structure on a metric space, arXiv:math/0608536v4, is a notion in between a group and a differential structure, accounting for the approximate self-similarity of the metric space. The basic objects of a dilatation structure are…
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
In this paper we introduce and study some mathematical structures on top of transitive Lie algebroids in order to formulate gauge theories in terms of generalized connections and their curvature: metrics, Hodge star operator and integration…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
Tropical algebraic geometry is an active new field of mathematics that establishes and studies some very general principles to translate algebro-geometric problems into purely combinatorial ones. This expository paper gives an introduction…
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique…
A description of a ring of functions on the base of a universal formal deformation for several moduli problems is given. The answer is given in terms of a homology group of a certain dg Lie algebra canonically (up to an essentially unique…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
Cohomologies of nonassociative metagroup algebras are investigated. Extensions of metagroup algebras are studied. Examples are given.
This book is expository and is in Russian. It is shown how in the course of solution of interesting geometric problems (close to applications) naturally appear main notions of algebraic topology (homology groups, obstructions and…
Algebraic geometry for groups and Lie algebraic has been recently defined and studied by many authors on the purpose to study set defined by algebraic equations on abstract groups and Lie algebras. The purpose of this paper is to present a…
The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems…
We survey the recent use of division algebras in wireless communication.
This text is an introduction to dilation surfaces. We attempt to expose some geometric and dynamical aspects of the subject: moduli spaces, directional foliations and the Teichm\"uller flow.
This paper describes a higher-categorical version of the theory of colored operads, giving applications to the study of commutative ring spectra.
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
We study algebraic and geometric properties of metric spaces endowed with dilatation structures, which are emergent during the passage through smaller and smaller scales. In the limit we obtain a generalization of metric affine geometry,…
The cohomology and deformation theory of 3-Lie algebras are revisited. The theory of extending structures and unified product for 3-Lie algebras are developed.It is proved that the extending structures of 3-Lie algebras can be classified by…
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…