Related papers: Ternary mappings of triangular algebras
Endomorphisms of the measure algebra of commutative hypergroups are investigated. We focus on derivations and higher order derivations which are closely related to moment function sequences of higher rank. We describe the exact connection…
We provide a clarification of the classification of two-dimensional algebras over an arbitrary base field. Using this clarification, we determine the number of non-isomorphic two-dimensional algebras over a finite field.
The theory of representations of Clifford algebras is extended to employ the division algebra of the octonions or Cayley numbers. In particular, questions that arise from the non-associativity and non-commutativity of this division algebra…
Higher derivations on an associative algebra generalizes higher order derivatives. We call a tuple consisting of an algebra and a higher derivation on it by an AssHDer pair. We define a cohomology for AssHDer pairs with coefficients in a…
In this survey, we first review some known results on the representation theory of algebras with triangular decomposition, including the classification of the simple modules. We then discuss a recipe to construct Hopf algebras with…
In the context of the integration over algebras introduced in a previous paper, we obtain several results for a particular class of associative algebras with identity. The algebras of this class are called self-conjugated, and they include,…
In this review we discuss what is known about semiorthogonal decompositions of derived categories of algebraic varieties. We review existing constructions, especially the homological projective duality approach, and discuss some related…
In this paper we describe graded automorphisms and antiautomorphisms of finite order on matrix algebras endowed with a group gradings by a finite abelian group over an arbitrary algebraically closed field of charcteristic different from 2.
We describe the images of multilinear polynomials of arbitrary degree evaluated on the $3\times 3$ upper triangular matrix algebra over an infinite field.
We give a conceptual explanation of universal deformation formulas for unital associative algebras and prove some results on the structure of their moduli spaces. We then generalize universal deformation formulas to other types of algebras…
A trinomial algebra is a commutative finitely generated algebra given by a system of compatible relations each of which is a polynomial with three terms. Such algebras arise as the Cox rings of varieties admitting a complexity one torus…
Parafermions of order two are shown to be the fundamental tool to construct ternary superspaces related to cubic extensions of the Poincar\'e algebra
We give a geometric classification of 4-dimensional superalgebras over an algebraic closed field.
A {\em $k$-trinitary algebra} is any subalgebra of the space of smooth functions $f: M \to {\mathbb R}$ that is distinguished in this space by $k$ independent conditions of the form $f(x_i) = f(\tilde x_i) = f(\hat x_i)$, where $x_i, \tilde…
We compute the transgressed forms of some modularly invariant characteristic forms,which are related to the twisted elliptic genera. We study the modularity properties of these secondary characteristic forms and relations among them. We…
We discuss an unusual phenomenon in (integral) positive ternary quadratic forms. We also describe an interesting pairing of genera of ternary forms.
We examine the heap of linear connections on anchored vector bundles and Lie algebroids. Naturally, this covers the example of affine connections on a manifold. We present some new interpretations of classical results via this ternary…
Given a ternary homogeneous polynomial, the fixed points of the map from $\mathbb{P}^2$ to itself defined by its gradient are called its eigenpoints. We focus on cubic polynomials, and analyze configurations of eigenpoints that admit one or…
In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…
In order to apply nonstandard methods to modern algebraic geometry, as a first step in this paper we study the applications of nonstandard constructions to category theory. It turns out that many categorial properties are well behaved under…