Related papers: Associative algebras in $CR$-geometry

The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…

We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.

In this paper, we give a purely cohomological interpretation of the extension problem for associative algebras; that is the problem of extending an associative algebra by another associative algebra. We then give a similar interpretation of…

For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…

Together with F. Morel, we have constructed in \cite{CR, Cobord1, Cobord2} a theory of {\em algebraic cobordism}, an algebro-geometric version of the topological theory of complex cobordism. In this paper, we give a survey of the…

We define several versions of the cohomology ring of an associative algebra. These ring structures unify some well known operations from homological algebra and differential geometry. They have some formal resemblance with the quantum…

Given a variety of universal algebras. A method is suggested for describing automorphisms of a category of free algebras of this variety. Applying this general method all automorphisms of such categories are found in two cases: 1) for the…

We give an algebro-geometric approach towards the dynamics of automorphisms/endomorphisms of projective varieties or compact K\"ahler manifolds, try to determine the building blocks of automorphisms /endomorphisms, and show the relation…

We classify the normal CR structures on $S^3$ and their automorphism groups. Together with [3], this closes the classification of normal CR structures on contact 3-manifolds. We give a criterion to compare 2 normal CR structures, and we…

A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…

We present an overview of the recent developments in the study of the classification problem for automorphisms of C*-algebras from the perspective of Borel complexity theory.

We study automorphism groups of formal matrix algebras. We also consider automorphisms of ordinary matrix algebras (in particular, triangular matrix algebras).

An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.

This is an extensive (published) survey on CR geometry, whose major themes are: formal analytic reflection principle; generic properties of Systems of (CR) vector fields; pairs of foliations and conjugate reflection identities; Sussmann's…

The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.

It is proved that a germ of a real analytic CR map from a smooth real-analytic minimal CR manifold M to an essentially finite real-algebraic generic submanifold M' of P^N of the same CR-dimension extends as a holomorphic correspondence…

We introduce the notion of skew-holomorphic Lie algebroid on a complex manifold, and explore some cohomologies theories that one can associate to it. Examples are given in terms of holomorphic Poisson structures of various sorts.

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 survey the development of Clifford's geometric algebra and some of its engineering applications during the last 15 years. Several recently developed applications and their merits are discussed in some detail. We thus hope to clearly…

In this paper, we study group equations with occurrences of automorphisms. We describe equational domains in this class of equations. Moreover, we solve a number of open problem posed in universal algebraic geometry.