Related papers: Special Algebraic Structures
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
New features of systems with non-trivial topology such as fractional quantum numbers, inequivalent quantizations, good operators, topological anomalies, etc. are described in the framework of an algebraic quantization procedure on a group.…
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…
In this text I present some problems which led to the introduction of special kinds of graphs as tools for studying singular points of algebraic surfaces. I explain how such graphs were first described using words, and how several…
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.
We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting…
We define a formal framework for the study of algebras of type Max-plus, Min-Plus, tropical algebras, and more generally algebras over a commutative idempotent semi-field. This work is motivated by the increasingly diversified use of these…
Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…
We first provide an overview of several results dealing with the genus of a division algebra and highlight the role of ramification in its analysis. We then give a survey of recent developments on the genus problem for simple algebraic…
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approaching them via model theory and algebraic geometry. Along…
The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also…
Information algebras arise from the idea that information comes in pieces which can be aggregated or combined into new pieces, that information refers to questions and that from any piece of information, the part relevant to a given…
A survey of special curves, special subvarieties of $\mathcal{M}_g$, and related topics. A large portion of the text discusses various possible interpretation of the word 'special' in this context by giving also concrete examples. One…
We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of…
In this paper we will relate hyperstructures and the general $\mathscr{H}$-principle to known mathematical structures, and also discuss how they may give rise to new mathematical structures. The main purpose is to point out new ideas and…
We introduce "synchronous algebras", an algebraic structure tailored to recognize automatic relations (aka. synchronous relations, or regular relations). They are the equivalent of monoids for regular languages, however they conceptually…
This survey article has two components. The first part gives a gentle introduction to Serre's notion of $G$-complete reducibility, where $G$ is a connected reductive algebraic group defined over an algebraically closed field. The second…
We lay down the foundations for a systematic study of differentiable and algebraic supervarieties, with a special attention to supergroups.
This paper lays out a foundation for a theory of supertropical algebraic geometry, relying on commutative $\nu$-algebra. To this end, the paper introduces $\mathfrak{q}$-congruences, carried over $\nu$-semirings, whose distinguished ghost…