Quantum Orthogonal Cayley-Klein Groups in Cartesian Basis

Abstract

The similarity transformations of quantum orthogonal groups are developed and FRT theory is reformulated to the Cartesian basis. The quantum orthogonal Cayley-Klein groups are introduced as the algebra functions over an associative algebra with the nilpotent generators. The quantum orthogonal Cayley-Klein algebras are obtained as the dual objects to the corresponding quantum groups.

Possible contractions of quantum orthogonal groups

“…For N = 2n from theorem 4 we obtain seven admissible contractions: j n−1 = 1, ι n−1 , j n = 1, ι n , j n+1 = 1, ι n+1 , where deformation parameter is multiplied by J = j n−1 j n j n+1 . It should be considered in papers [21], [25] just these allowed contractions.…”

New Approaches on Dual Space

“…In recent years, dual numbers have been widely used in kinematics, dynamics, mechanism design, and field and group theories ( [5], [6], [7], [8] and [12]). For example in kinematics, constraint manifolds of spatial mechanisms are explained using dual numbers system [10].…”

General dual boosts in lorentzian dual plane D2 1

“…There has been many applications of dual numbers in recent years, such as; in robotics, dynamics, and kinematics ( [17], [7], [16]), in computer aided geometrical design and modelling of rigid bodies, mechanism design ( [2], [4], [3], [14]), in …eld theory ( [6], [19], [1]), and in group theory ( [9], [10], [11]).…”