Related papers: Ternary mappings of triangular algebras
We study the automorphism groups of finite-dimensional cyclic Leibniz algebras. In this connection, we consider the relationships between groups, modules over associative rings and Leibniz algebras.
We give an explicit description of the Lie algebra of derivations for a class of infinite dimensional algebras which are given by \'etale descent. The algebras under consideration are twisted forms of central algebras over rings, and…
In this paper, we study metric completions of triangulated categories in a representation-theoretic context. We provide a concrete description of completions of bounded derived categories of hereditary finite dimensional algebras of finite…
We introduce a notion of Pre-structurable Algebras based upon triality relations and study its relation to structurable algebra of Allison, as well as to Lie algebras satisfying triality.
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
Let $\A$ be an algebra and $\sigma$ an automorphism of $\A$. A linear map $d$ of $\A$ is called a $\sigma$-derivation of $\A$ if $d(xy) = d(x)y + \sigma(x)d(y)$, for all $x, y \in \A$. A bilinear map $D: \A \times \A \to \A$ is said to be a…
An algebraic deformation theory of module-algebras over a bialgebra is constructed. The cases of module-coalgebras, comodule-algebras, and comodule-coalgebras are also considered.
Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, Dugger-Shipley, ..., Toen and…
We develop a unified framework for the study of properties involving diagonalizations of dense families in topological spaces. We provide complete classification of these properties. Our classification draws upon a large number of methods…
Differential categories provide the categorical foundations for the algebraic approaches to differentiation. They have been successful in formalizing various important concepts related to differentiation, such as, in particular,…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
In this article, we give a new class of automorphisms of Leavitt path algebras of arbitrary graphs. Consequently, we obtain Anick type automorphisms of these Leavitt path algebras and new irreducible representations of Leavitt algebras of…
The precise formulation of derivation for tree-adjoining grammars has important ramifications for a wide variety of uses of the formalism, from syntactic analysis to semantic interpretation and statistical language modeling. We argue that…
We introduce a linear algebraic object called a bidiagonal triple. A bidiagonal triple consists of three diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the…
These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.
We consider a new class of quaternionic mappings, associated with the spatial partial differential equations. We describe all mappings from this class using four analytic functions of the complex variable.
This is the first of series of talks presented at a permanent Rutgers workshop on noncommutative algebra and geometry. We study here quadratic and quadratic-linear algebras defined by factorizations of noncommutative polynomials and…
After a short introduction on the theory of homogeneous algebras we describe the application of this theory to the analysis of the cubic Yang-Mills algebra, the quadratic self-duality algebras, their "super" versions as well as to some…
In this paper, we give the definition of the generalized Ramond N=2 superconformal algebras and discuss the derivation algebra and the automorphism group
In the paper I considered mappings of conjugation of quaternion algebra. I proved the theorem that there is unique expansion of R-linear mapping of quaternion algebra relative to the given set of mappings of conjugation.