Unified framework for unit-norm elements in quaternion, biquaternion, dual quaternion and split biquaternion algebras representing isometries, yielding a new decomposition of 4D rotations.
The representation of physical motions by various types of quaternions
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abstract
It is shown that the groups of Euclidian rotations, rigid motions, proper, orthochronous Lorentz transformations, and the complex rigid motions can be represented by the groups of unit-norm elements in the algebras of real, dual, complex, and complex dual quaternions, respectively. It is shown how someof the physically-useful tensors and spinors can be represented by the various kinds of quaternions. The basic notions of kinematical states are described in each case, except complex dual quaternions, where their possible role in describing the symmetries of the Maxwell equations is discussed.
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math.RA 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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Some extensions of quaternions and symmetries of simply connected space forms
Unified framework for unit-norm elements in quaternion, biquaternion, dual quaternion and split biquaternion algebras representing isometries, yielding a new decomposition of 4D rotations.