We derive an appropriate definition of transpose for quaternionic matrices and give a new panoramic review of the quaternionic groups. We aim to analyse possible quaternionic groups for GUTs.

We present details of the harmonic space construction of a quaternionic extension of the four-dimensional Taub-NUT metric. As the main merit of the harmonic space approach, the metric is obtained in an explicit form following a generic set of rules. It exhibits SU(2) × U(1) isometry group and depends on two parameters, TaubNUT ‘mass’ and the cosmological constant. We consider several limiting c...

We construct left invariant quaternionic contact (qc) structures on Lie groups with zero and non-zero torsion and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of non-flat quaternionic contact manifolds. We prove that the product of the real line with a seven dimensional manifold, equipped with a certain qc structure, has a quaternionic Kähler me...

There exist many four dimensional integrable theories. They include self-dual gauge and gravity theories, all their extended supersymmetric generalisations, as well the full (non-self-dual) N=3 super Yang-Mills equations. We review the harmonic space formulation of the twistor transform for these theories which yields a method of producing explicit connections and metrics. This formulation uses...

This paper uses results on the classification of minimal triangulations of 3-manifolds to produce additional results, using covering spaces. Using previous work on minimal triangulations of lens spaces, it is shown that the lens space L(4k,2k − 1) and the generalised quaternionic space S/Q4k have complexity k, where k ≥ 2. Moreover, it is shown that their minimal triangulations are unique. AMS ...

We analyze the hypermultiplet moduli space describing the universal sector of type IIA theory compactified on a Calabi-Yau threefold. The classical moduli space is described in terms of the coset SU(2, 1)/U(2). The flux quantization condition of the antisymmetric tensor field of M-theory implies discrete identifications for the scalar fields describing this four-dimensional quaternionic geometr...

We introduce quaternionic Gabor filters for the classification of local image structure. These filters are constructed as windowed basis functions of the quaternionic Fourier transform. We show that – in contrast to the 2D complex Gabor filters – the quaternionic Gabor filters are intrinsically 2D filters. A generalized phase concept is introduced and compared to the classical one. It is shown ...

A tensor invariant is defined on a quaternionic contact manifold in terms of the curvature and torsion of the Biquard connection involving derivatives up to third order of the contact form. This tensor, called quaternionic contact conformal curvature, is similar to the Weyl conformal curvature in Riemannian geometry and to the Chern-Moser tensor in CR geometry. It is shown that a quaternionic c...

We review here the microcanonical and canonical ensembles constructed on an underlying generalized quantum dynamics and the algebraic properties of the conserved quantities. We discuss the structure imposed on the microcanonical entropy by the equilibrium conditions. 1 1. Introduction In this paper we review briefly the generalized quantum dynamics 1,2 constructed on a phase space of local nonc...