In this paper, we established the connection between generalized quaternion algebra and real (complex) matrix algebras by using Hamilton operators. We obtained complex matrices corresponding to basis of quaternions. Also, investigated features matrices. get Pauli Then, have shown that produced these is isomorphic Clifford Cl(E_αβ^3) space E_αβ^3.
 Finally, studied relations among symplecti...

We show that the Lorentz covariant formulation of N = 2 string in a curved space reveals an explicit hyper–Kähler structure. Apart from the metric, the superconformal currents couple to a background two–form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra. P...

Let X be the Shimura curve corresponding to the quaternion algebra over ramified only at 3 and 13. B. Jordan showed that X ( √ −13) is a counterexample to the Hasse principle. Using an equation of X found by A. Kurihara, it is shown here, by elementary means, that X has no ( √ −13)-rational divisor classes of odd degree. A corollary of this is the fact that this counterexample is explained by t...

New, efficient, 8-D rotation CORDIClike algorithms for matrix computations are presented. These algorithms are a natural extension to 8 dimensions of Quaternion CORDIC algorithms, offered by J.M. Delosme and S.F. Hsiao. This leads to significantly reduced computations in contrast to 8-D Householder CORDIC algorithms given by the same authors. Such algorithms may be utilized for designing VLSI a...

We build the q = −1 defomation of plane on a product of two copies of algebras of functions on the plane. This algebra constains a subalgebra of functions on the plane. We present general scheme (which could be used as well to construct quaternion from pairs of complex numbers) and we use it to derive differential structures, metric and discuss sample field theoretical models. TPJU 4/95 Februar...

We show that the Lorentz covariant formulation of N = 2 string in a curved space reveals an explicit hyper–Kähler structure. Apart from the metric, the superconformal currents couple to a background two–form. By superconformal symmetry the latter is constrained to be holomorphic and covariantly constant and allows one to construct three complex structures obeying a (pseudo)quaternion algebra. P...

The additive identity is (0, 0), the multiplicative identity is (1, 0), and from addition and scalar multiplication of real vectors we have (a, b) = (a, 0) + (0, b) = a(1, 0) + b(0, 1), which looks like a+ bi if we define i to be (0, 1). Real numbers occur as the pairs (a, 0). Hamilton asked himself if it was possible to multiply triples (a, b, c) in a nice way that extends multiplication of co...

The Lee-Friedrichs model has been very useful in the study of decay-scattering systems in the framework of complex quantum mechanics. Since it is exactly soluble, the analytic structure of the amplitudes can be explicitly studied. It is shown in this paper that a similar model, which is also exactly soluble, can be constructed in quaternionic quantum mechanics. The problem of the decay of an un...

This paper introduces a new intractable security problem whose intractability is due to the NP completeness of multivariate quadratic problem. This novel problem uses quaternion algebra in conjunction with MQ. Starting with the simultaneous multivariate equations, we transform these equations into simultaneous quaternion based multivariate quadratic equations. A new scheme for computational zer...

Introduction In a manuscript on mod representations attached to modular forms [26], the author introduced an exact sequence relating the mod p reduction of certain Shimura curves and the mod q reduction of corresponding classical modular curves. Here p and q are distinct primes. More precisely, fix a maximal order O in a quaternion algebra of discriminant pq over Q. Let M be a positive integer ...