Related papers: Non-associative algebraic structures: classificati…
This is the abstract of a series of lectures given during the XIIIth School on Geometry and Physics, Bialystok (Poland), in July 2024. In this minicourse, we first examine the algebraic aspects of barycentric algebras. Then, we focus on…
I summarize some of the ideas and motivations behind a recently performed conformal field theory analysis of closed strings in both geometric and nongeometric three-form flux backgrounds. This suggests an underlying nonassociative structure…
The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations with polynomial homogeneous right-hand…
These lecture notes were written during a mini-course on noncommutative Lp-spaces at the Basque Center of Applied Mathematics. It starts presenting the theory of weights and traces in von Neumann algebra, followed by the theory of…
In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
This survey paper, written in spanish, is an extended version of lecture notes for a mini-course taught at the 2022 Summer School in Geometric Group Theory, which took place in the Centro de Ciencias Matem\'aticas in Morelia, Mexico in July…
In this paper we show that non abelian extensions of an associative algebra $\mathcal{B}$ by an associative algebra $\mathcal{A}$ can be viewed as Maurer-Cartan elements of a suitable differential graded Lie algebra $L$. In particular we…
We present classes of nonassociative algebras whose associator satisfies invariance conditions given by the action of the 3 order symmetric group. Amongst these algebras we find the wellknown Pre Lie or Vinberg algebras and the Lie…
A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and…
In this paper we consider all these nonassociative algebras defined by the action of invariant subspaces of the symmetric group $\Sigma_3$ on the associator of the considered laws.
Numerical characteristics of identities of finite-dimensional nonassociative algebras are studied. The main result is the construction of a four-dimensional simple unitary algebra with fractional PI-exponent strictly less than its…
Recently delivered lectures on Self-Referential Mathematics, [2], at the Department of Mathematics and Applied Mathematics, University of Pretoria, are briefly presented. Comments follow on the subject, as well as on Inconsistent…
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,…
This thesis examines some of the applications of scaling relations in understanding non linear structure formation.
A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the…
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
These are the lecture notes from my short course of the same title at the CIMPA Research School on Associative and Nonassociative Algebras and Dialgebras: Theory and Algorithms - In Honour of Jean-Louis Loday (1946-2012), held at CIMAT,…
We present an unified construction for algebras and modules homologies and cohomologies, in the case of associative, commuttaive, Lie and Gerstenhaber algebras. We make a distinction between the linear part of the construction of algebras…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…