Related papers: Polyadization of algebraic structures
The polysymplectic $(n+1)$-form is introduced as an analogue of the symplectic form for the De Donder-Weyl polymomentum Hamiltonian formulation of field theory. The corresponding Poisson brackets on differential forms are constructed. The…
This is a report on recent progress concerning the interactions between derived algebraic geometry and deformation quantization. We present the notion of derived algebraic stacks, of shifted symplectic and Poisson structures, as well as the…
First we introduce a generalization of symmetric spaces to parabolic geometries. We provide construction of such parabolic geometries starting with classical symmetric spaces and we show that all regular parabolic geometries with smooth…
We define a new notion of an algebraic model structure, in which the cofibrations and fibrations are retracts of coalgebras for comonads and algebras for monads, and prove "algebraic" analogs of classical results. Using a modified version…
We introduce an object that has obvious similarity to the classical one - the algebra of supersymmetric polynomials. Despite the similarity, the known structure theorems on supersymmetric polynomials do not help in the study of the new…
In this expository article, we give a self-contained introduction to the wonderfully well-behaved class of pseudocompact algebras, focusing on the foundational classes of semisimple and separable algebras. We give characterizations of such…
This paper establishes a uniform procedure to split the operations in any algebraic operad, generalizing previous known notions of splitting algebraic structures from the dendriform algebra of Loday that splits the associative operation to…
In~\cite{algorithmic} was given an algorithm that computes arithmetical structures on matrices. We use some of the ideas contained there to get an algorithm that computes arithmetical structures over dominated polynomials. A dominated…
The prolongation structure of a two-by-two problem is formulated very generally in terms of exterior differential forms on a standard representation of Pauli matrices. The differential system is general without making reference to any…
The algebra of so-called shifted symmetric functions on partitions has the property that for all elements a certain generating series, called the $q$-bracket, is a quasimodular form. More generally, if a graded algebra $A$ of functions on…
Using the concept of mixable shuffles, we formulate explicitly the quantum quasi-shuffle product, as well as the subalgebra generated by primitive elements of the quantum quasi-shuffle bialgebra. We construct a braided coalgebra structure…
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…
In this note we first consider a ternary matrix group related to the von Neumann regular semigroups and to the Artin braid group (in an algebraic way). The product of a special kind of ternary matrices (idempotent and of finite order)…
This is a simple way rigorously to construct Grassmann, Clifford and Geometric Algebras, allowing degenerate bilinear forms, infinite dimension, using fields or certain modules (characteristic 2 with limitation) - and characterize the…
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…
We study the problem of modeling a binary operation that satisfies some algebraic requirements. We first construct a neural network architecture for Abelian group operations and derive a universal approximation property. Then, we extend it…
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
In this thesis quadratic and cubic algebras, which are extensions of SU(1,1) and SU(2) are studied in detail, with particular attention being given to their construction, their finite and infinite dimensional irreducible representations and…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
There is a classical connection between the representation theory of the symmetric group and the general linear group called Schur-Weyl duality. Variations on this principle yield analogous connections between the symmetric group and other…