47 research outputs found
Nonassociative geometry: Towards discrete structure of spacetime
In the framework of nonassociative geometry (hep-th/0003238) a unified
description of continuum and discrete spacetime is proposed. In our approach at
the Planck scales the spacetime is described as a so-called "diodular discrete
structure" which at large spacetime scales `looks like' a differentiable
manifold. After a brief review of foundations of nonassociative geometry,we
discuss the nonassociative smooth and discrete de Sitter spacetimes.Comment: RevTex file, 5 pages, typos correcte
Loop geometries
We introduce the construction of the semidirect product of a loop and its associate (or quasigroup)-the group uniquely generated by the loop. For a (left or right) loop the semidirect product is a group acting transitively on the loop so that the loop is provided with the structure of a homogeneous space, the stationary subgroup being its associate. The construction is reversible, viz. any homogeneous space can be provided with the structure of a loop so that the semidirect product of it with the transassociate is isomorphic with the fundamental group of the homogeneous space and the transassociate is isomorphic with the stationarity group. © 1973 Consultants Bureau
Quasigroups, Geometry and Nonlinear Geometric Algebra
A survey of the methods of the theory of quasigroups and loops in algebra and geometry is presented in order to attract the attention of mathematicians and physicists to promising applications of this new branch of mathematics in applied sciences