A viable formulation of gauge theory with extra generations in terms of quaternionic fields is presented. For the theory to be acceptable, the number of generations should be equal to or greater than 4. The quark-lepton mass matrices are generalized into quaternionic matrices. It is concluded that explicit CP violation automatically disappears in both strongand weak-interaction sectors. ∗e-mail...

We prove a version of Shimizu’s lemma for quaternionic hyperbolic space. Namely, consider groups of quaternionic hyperbolic isometries containing a parabolic map fixing infinity. We show that any element of such a group not fixing infinity has an isometric sphere whose radius is bounded by a function of the parabolic translation length at its centre. Mathematics Subject Classifications (2000): ...

We study the moduli space of quaternionic Kähler structures on a compact manifold of dimension 4n ≥ 12 from a point of view of Riemannian geometry, not twistor theory. Then we obtain a rigidity theorem for quaternionic Kähler structures of nonzero scalar curvature by observing the moduli space.

In this paper the geometry of two-qubit systems under local unitary group SO(2) ⊗ SU(2) is discussed. It is shown that the quaternionic conformal map intertwines between this local unitary subgroup of Sp(2) and the quaternionic Möbius transformation which is rather a generalization of the results of Lee et al (2002 Quantum Inf. Process. 1 129).

We present some striking global consequences of a model quaternionic quantum eld theory which is locally complex. We show how making the quaternionic structure a dynamical quantity naturally leads to the prediction of cosmic strings and non-baryonic hot dark matter candidates. Report Number: UM{P{96/88; RCHEP 96/11. Typeset using REVTEX

We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems. When applied to the quaternionic Wigner and Wishart families of random matrices the result gives the duality between moments of these families and the corresponding real Wigner and Wishart families.

It is shown that there is no continuous map from the quaternionic Grassmannian Grk,n(k ≥ 2, n ≥ k + 2) to the quaternionic projective space HP ∞ such that the pullback of the first Pontryagin class of the tautological bundle over HP is equal to the first Pontryagin class of the tautological bundle over Grk,n. In fact some more precise statement is proved.

The functions studied in the paper are quaternion-valued of a quaternionic variable. It is shown that left slice regular and right related by particular involution, intrinsic play central role theory functions. relation between functions, revealed. As an application, classical Laplace transform generalized naturally to quaternions two different ways, which function real variable or function. us...

When n is even, orthogonal spreads in an orthogonal vector space of type O-(2n 2,2) are used to construct line-sets of size (2nm1 + 1)2”-’ in W2”~’ all of whose angles are 90” or cos -1(2-(“-2)/2). These line-sets are then used to obtain quatemionic Kerdock Codes. These constructions are based on ideas used by Calderbank, Cameron, Kantor, and Seidel in real and complex spaces.