Related papers: Introduction to universal algebra and clones
This is an introduction to quantum algebra, from a geometric perspective. The classical spaces $X$, such as the Lie groups, homogeneous spaces, or more general manifolds, are described by various algebras $A$, defined over various fields…
These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.
We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background on the theory of cluster algebras, and discuss the interplay with cluster categories and cluster tilted algebras.
General concept of ternary algebras is introduced in this article, along with several examples of its realization. Universal envelope of such algebras is defined, as well as the concept of tri-modules over ternary algebras. The universal…
This is a preliminary draft of Chapters 1-3 of our forthcoming textbook "Introduction to Cluster Algebras." This installment contains: Chapter 1. Total positivity Chapter 2. Mutations of quivers and matrices Chapter 3. Clusters and seeds
A field algebra is a ``non-commutative'' generalization of a vertex algebra. In this paper we develop foundations of the theory of field algebras.
We obtain a complete classification of minimal simple unitary $W$-algebras.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
An elementary introduction to the principles of algebraic surgery.
This is the compendium of the cluster algebra and quiver package for sage. The purpose of this package is to provide a platform to work with cluster algebras in graduate courses and to further develop the theory by working on examples, by…
The article presents some aspects on the use of computer in teaching general relativity for undergraduate students with some experience in computer manipulation. The article presents some simple algebraic programming (in REDUCE+EXCALC…
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 aim of this article is to introduce Hall bases of free Leibniz algebras. We modify the classical notion of Hall bases for free Lie algebras in order to provide the similar construction for the case of Leibniz algebras.
A simple pedagogical introduction to the Colombeau algebra of generalised functions is presented, leading the standard definition.
A clone on a set X is a set of finitary operations on X which contains all projections and which is moreover closed under functional composition. Ordering all clones on X by inclusion, one obtains a complete algebraic lattice, called the…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
This brief note, written for non-specialists, aims at drawing an introductive overview of the multiverse issue.
The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…
Abstraction is key to human and artificial intelligence as it allows one to see common structure in otherwise distinct objects or situations and as such it is a key element for generality in AI. Anti-unification (or generalization) is…