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Riemannian and Absolute Parallelism (AP) geometries are discussed. A lavish treatment of path equations in the AP-space using the Bazanski-type Lagrangian is presented; We write down an expression that is absolutely conserved along a curve…
Two successive generalizations of the usual tensor products are given. One can be constructed for arbitrary binary operations, and not only for semigroups, groups or vector spaces. The second one, still more general, is constructed for…
We present the basic concepts of tensor products of vector spaces, emphasizing linear algebraic and combinatorial techniques as needed for applied areas of research. The topics include (1) Introduction; (2) Basic multilinear algebra; (3)…
Absolute parallelism geometry is frequently used for physical applications. It has two main defects, from the point of view of applications. The first is the identical vanishing of its curvature tensor. The second is that its autoparallel…
This paper suggests an algebraic version of the theorem on the existence of eigenvectors for linear operators in abstract idempotent spaces. Earlier, the theorem on the existence of eigenvectors was only known for the cases of a free…
A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in…
After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.
Irregularities in the metric tensor of a signature-changing space-time suggest that field equations on such space-times might be regarded as distributional. We review the formalism of tensor distributions on differentiable manifolds, and…
Transit functions were introduced as models of betweenness on undirected structures. Here we introduce directed transit function as the directed analogue on directed structures such as posets and directed graphs. We first show that…
In this paper, some left-symmetric algebras are constructed from linear functions. They include a kind of simple left-symmetric algebras and some examples appearing in mathematical physics. Their complete classification is also given, which…
A tensor is a multi-way array that can represent, in addition to a data set, the expression of a joint law or a multivariate function. As such it contains the description of the interactions between the variables corresponding to each of…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
We study the connection between two combinatorial notions associated to a quiver: the quiver algebra and the path coalgebra. We show that the quiver coalgebra can be recovered from the quiver algebra as a certain type of finite dual, and we…
We associate with the Grassmann algebra a topological algebra of distributions, which allows the study of processes analogous to the corresponding free stochastic processes with stationary increments, as well as their derivatives.
This paper classifies the derivations of group algebras in terms of the generators and defining relations of the group. If $RG$ is a group ring, where $R$ is commutative and $S$ is a set of generators of $G$ then necessary and sufficient…
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
We realize the free dendriform trialgebra on one generator, as well as several other examples of dendriform trialgebras, as sub-trialgebras of an algebra of noncommutative polynomials in infinitely many variables.
Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…
Using the Schwinger-Keldysh technique, we derive the transport equations for a system of quantum scalar fields. We first discuss the general structure of the equations and then their collision terms. Taking into account up to three-loop…
In this paper we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras, and describe…