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We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
This paper deals with stratifying systems over hereditary algebras. In the case of tame hereditary algebras we obtain a bound for the size of the stratifying systems composed only by regular modules and we conclude that stratifying systems…
Let A be a geometric arrangement such that codim(x) > 1 for every x in A. We prove that, if the complement space M(A) is rationally hyperbolic, then there exists an injective from a free Lie algebra L(u,v) to the homotopy Lie algebra of…
We study a family of interacting bosonic representations of the N=2 superconformal algebra. These models can be tensored with a conjugate theory to give the free theory. We explain how to use free fields to study interacting fields and…
We give conjectures on the "asymptotic" behaviour of the Hilbert series of (quotients by) generic ideals in the exterior algebra, as the number of variables tend to infinity. Our conjectures are supported by extensive computer calculations.
In this paper, we present an approach for modeling bio-tissues that incorporates the variability in properties as part of their characteristics. This is achieved by considering the parameters of the model of a biomaterial to themselves be…
In this paper we extend the idea of integration to generic algebras. In particular we concentrate over a class of algebras, that we will call self-conjugated, having the property of possessing equivalent right and left multiplication…
In decision theory an act is a function from a set of conditions to the set of real numbers. The set of conditions is a partition in some algebra of events. The expected value of an act can be calculated when a probability measure is given.…
Some algebraic, geometric and geometroalgebraic characteristics of pairs of operators are discussed.
In this report, we study the algebraic geometry aspect of Hofstadter type models through the algebraic Bethe equation. In the diagonalization problem of certain Hofstadter type Hamiltonians, the Bethe equation is constructed by using the…
A basic finite dimensional algebra over an algebraically closed field $k$ is isomorphic to a quotient of a tensor algebra by an admissible ideal. The category of left modules over the algebra is isomorphic to the category of representations…
This paper studies the properties of two kinds of matroids: (a) algebraic matroids and (b) finite and infinite matroids whose ground set have some canonical symmetry, for example row and column symmetry and transposition symmetry. For (a)…
Let $A$ be a finite dimensional algebra over an algebraically closed field $k$, $\mathcal {D}^b(A)$ be the bounded derived category of $A$-mod and $A^{(m)}$ be the $m$-replicated algebra of $A$. In this paper, we investigate the structure…
A strong link between information geometry and algebraic statistics is made by investigating statistical manifolds which are algebraic varieties. In particular it it shown how first and second order efficient estimators can be constructed,…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
We introduce the notion of the algebraic overshear density property which implies both the algebraic notion of flexibility and the holomorphic notion of the density property. We investigate basic consequences of this stronger property, and…
We define lifting properties for universal algebras, which we study in this general context and then particularize to various such properties in certain classes of algebras. Next we focus on residuated lattices, in which we investigate…
We prove that if, for a nontrivial variety of non-associative algebras, every subalgebra of every free algebra is free and $I^2$ is an ideal whenever $I$ is an ideal, then this variety coincides with the variety of all Lie algebras.
The purpose of this paper is to study the relationships between an $n$-Hom-Lie algebra and its induced $(n+1)$-Hom-Lie algebra. We provide an overview of the theory and explore the structure properties such as ideals, center, derived…
Let $(W,S)$ be a Coxeter system. A $W$-graph encodes a representation of the Hecke algebra $\mathcal{H}$ of $W$. We construct universal representations of multi-parameter Hecke algebras on certain quotients of path algebras, and study their…