Octonionic representations of GL(8,R) and GL(4,C)

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

Octonionic Aspects of Supergravity

An Octonionic Gauge Theory

The nonassociativity of the octonion algebra necessitates a bimodule representation, in which each element is represented by a left and a right multiplier. This representation can then be used to generate gauge transformations for the purpose of constructing a field theory symmetric under a gauged octonion algebra, the nonassociativity of which appears as a failure of the representation to clos...

Octonionic Gravitational Instantons

We construct eight-dimensional gravitational instantons by solving appropriate selfduality equations for the spin-connection. The particular gravitational instanton we present has Spin(7) holonomy and, in a sense, it is the eight-dimensional analog of the Eguchi-Hanson 4D space. It has a removable bolt singularity which is topologically S4 and its boundary at infinity is the squashed S7. We als...

Octonionic Reformulation of Vector Analysis

According to celebrated Hurwitz theorem, there exists four division algebras consisting of R (real numbers), C (complex numbers), H (quaternions) and O (octonions). Keeping in view the utility of octonion variable we have tried to extend the three dimensional vector analysis to seven dimensional one. Starting with the scalar and vector product in seven dimensions, we have redefined the gradient...