Dual quaternion algebra and its application to robotics have attracted considerable interest in the last two decades. quaternions great geometric appeal easily capture physical phenomena inside an algebraic framework, which is useful for both robot modeling control. Mathematical objects, such as points, lines, planes, infinite cylinders, spheres, coordinate systems, twists, wrenches, are all we...

Associated to any complex simple Lie algebra is a non-reductive complex Lie algebra which we call the intermediate Lie algebra. We propose that these algebras can be included in both the magic square and the magic triangle to give an additional row and column. The extra row and column in the magic square correspond to the sextonions. This is a six-dimensional subalgebra of the split octonions w...

A split hypercomplex learning algorithm for the training of nonlinear finite impulse response adaptive filters for the processing of hypercomplex signals of any dimension is proposed. The derivation strictly takes into account the laws of hypercomplex algebra and hypercomplex calculus, some of which have been neglected in existing learning approaches (e.g. for quaternions). Already in the case ...

We investigate doubled (generalized) complex structures in $2D$-dimensional Born geometries where T-duality symmetry is manifestly realized. show that K\"{a}hler, hyperk\"{a}hler, bi-hermitian and bi-hypercomplex of spacetime are implemented as structures. find the generalized K\"{a}hler (hyperk\"{a}hler) appear subalgebras bi-quaternions split-tetra-quaternions. parts these classified by Cliff...

The twistor space Z of self-dual positive Einstein manifolds naturally admits two 1-parameter families of Riemannian metrics, one is the family of canonical deformation metrics and the other is the family introduced by B. Chow and D. Yang in [C-Y]. The purpose of this paper is to compare these two families. In particular we compare the Ricci tensor and the behavior under the Ricci flow of these...

In this study, we introduce a new class of generalized quaternions whose components are dual-generalized complex Horadam numbers. We investigate some algebraic properties them.