相关论文: On the algebraic classification of spacetimes

A complete classification of two-dimensional algebras over algebraically closed fields is provided

The algebraic and geometric classification of all complex $3$-dimensional transposed Poisson algebras is obtained. Also, we discuss strong special $3$-dimensional transposed Poisson algebras.

A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.

The Catalogue of Spacetimes is a collection of four-dimensional Lorentzian spacetimes in the context of the General Theory of Relativity (GR). The aim of the catalogue is to give a quick reference for students who need some basic facts of…

We give the algebraic and geometric classification of complex four-dimensional Jordan superalgebras. In particular, we describe all irreducible components in the corresponding varieties.

Spacetimes have conventionally been described by a global Lorentzian metric on a differentiable four-manifold. Herein we explore the possibility of spacetimes defined by a connection, which is locally but not globally Levi-Civita. The…

It is well known that the classification of the Weyl tensor in Lorentzian manifolds of dimension four, the so called Petrov classification, was a great tool to the development of general relativity. Using the bivector approach it is shown…

The dimensional structure of space-time is investigated according to physical and mathematical methods. We show that ther are various empirical and theoretical restrictions on the number of independent dimensions of space-time, consequently…

We present a general method which can be used for geometrical and physical interpretation of an arbitrary spacetime in four or any higher number of dimensions. It is based on the systematic analysis of relative motion of free test…

The Bel-Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov-Bel classification of the Weyl tensor. The new classes…

A category which generalises to higher dimensions many of the features of the Temperley-Lieb category is introduced.

In this paper the Weyl tensor is used to define operators that act on the space of forms. These operators are shown to have interesting properties and are used to classify the Weyl tensor, the well known Petrov classification emerging as a…

The notion of $\delta$-Novikov algebras was introduced recently as a generalization of Novikov and bicommutative algebras. It looks like $\delta$-Novikov algebras have a richer structure than Novikov algebras. So, unlike Novikov algebras,…

A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of…

The paper proposes a 4-dimensional generalization of the Hamilton equations of motion to the case of the Minkowski space-time. The approach can be applied to quantum as well as to classical, non-relativistic as well as relativistic…

Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the standard model and grand unified theories. Less discussed has been the question of why such…

We describe spinors in Minkowskian spaces with arbitrary signature and their role in the classification of space-time superalgebras and their R-symmetries in any dimension.

A classification of all four-dimensional power-commutative real division algebras is given. It is shown that every four-dimensional power-commutative real division algebra is an isotope of a particular kind of a quadratic division algebra.…

We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…

For Petrov D vacuum spaces, two simple identities are rederived and some new identities are obtained, in a manageable form, by a systematic and transparent analysis using the GHP formalism. This gives a complete involutive set of tables for…