Related papers: An Invitation to Noncommutative Algebra
The purpose of this paper is to give a notion of deformation of expressions for elements of algebra. Deformation quantization (cf.[BF]) deforms the commutative world to a non-commutative world. However, this involves deformation of…
The main aim of this paper to show how commutative algebra is connected to topology. We give underlying topological idea of some results on completable unimodular rows.
Application of the noncommutative geometry to several physical models is considered.
Homological algebra is often understood as the translator between the world of topology and algebra. However, this branch of mathematics is worth studying by itself, given that it provides fascinating perspectives about other disciplines,…
The paper deals with the configuration of subalgebras in generic $n$-dimensional $k$-argument anticommutative algebras and ``regular'' anticommutative algebras.
To a differential graded algebra with coefficients in a noncommutative algebra, by dualisation we associate an $A_\infty$-category whose objects are augmentations. This generalises the augmentation category of Bourgeois and Chantraine to…
The article is designed to explain to commutative algebraists what spectra (in the sense of algebraic topology) are, why they were originally defined, and how they can be useful for commutative algebra.
This is a survey of results on partially commutative groups and partially commutative algebras.
The non-commutative algebraic analog of the moduli of vector and covector fields is built. The structure of moduli of derivations of non-commutative algebras are studied. The canonical coupling is introduced and the conditions for…
These lectures notes are an intoduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate…
In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics,…
This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.
This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a…
By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via…
The present paper are the notes of a mini-course addressed mainly to non-experts. It purpose it to provide a first approach to the theory of mapping class groups of non-orientable surfaces.
Positively graded algebras are fairly natural objects which are arduous to be studied. In this article we query quotients of non-standard graded polynomial rings with combinatorial and commutative algebra methods.
We survey commutative and non-commutative analogs of uniform algebras in the Archimedean settings and also offer some non-Archimedean examples. Constraints on the development of non-complex uniform algebras are also discussed.
In this short article accessible for non-experts I discuss possible ways of constructing a non-commutative gravity paying special attention to possibilities of realizing the full diffeomorphism symmetry and to relations with 2D gravities.
The $2n$ dimensional manifold with two mutually commutative operators of differentiation is introduced. Nontrivial multidimensional integrable systems connected with arbitrary graded (semisimple) algebras are constructed. The general…
This is a kind of introduction to some basic topics in analysis, some of which would be covered in standard graduate courses, and some not. However, an important difference is that not much in the way of prerequisites are needed, beyond…