August 4, 2025Open Access

Quaternions Without Imaginarities or the Vector Representation of Quaternions

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This work demonstrates a new geometric property in quaternions using vectors instead of imaginary units, indicating innovative algebraic structures.

The study introduces a non-commutative product for quaternions, replacing imaginary units with vectors.
A Hamiltonian-adapted vector product is developed, showing versatility in quaternionic operations.
A new geometric property related to the vector product is established through the research.
The findings provide insights into the algebraic structure of quaternions, impacting theoretical applications.

Wolf‐Dieter Richter (2025) studied this question.

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This work demonstrates a new geometric property in quaternions using vectors instead of imaginary units, indicating innovative algebraic structures.