We invite discussions, suggestions, and collaborations on the following: Mathematics is the mother of all the sciences, engineering and technology, and a normed division algebra of all dimensions is the holy grail of mathematics. Singh along with Prof. SD Joshi (IIT Delhi) and Prof. Anubha Gupta (IIIT Delhi) developed normed division algebra of all dimensions which is available in preprint at: https://doi.org/10.13140/RG.2.2.18553.65120/3
A summary of "On the hypercomplex numbers and normed division algebra of all dimensions: A unified multiplication":
Key Points:
- Expanding Number Systems: The paper proposes a way to create hypercomplex numbers (numbers with more than two dimensions) that extend the traditional complex numbers.
- Overcoming Dimension Limitations: It challenges the previous belief that only four real division algebras exist (with dimensions 1, 2, 4, and 8).
- Unified Multiplication: It introduces a new multiplication method, called "scaling and rotative multiplication," that enables the formation of normed division algebras in any finite dimension.
- Key Properties:These hypercomplex number systems are non-distributive, meaning that the usual distributive property of multiplication over addition doesn't hold. They are compatible with existing multiplication for dimensions 1 and 2, meaning they smoothly extend complex numbers.
Potential Implications:
- Broader Mathematical Applications: This work could lead to new developments in various mathematical fields, such as abstract algebra, geometry, and analysis.
- New Frontiers in Physics and Engineering: Hypercomplex numbers have a history of applications in physics and engineering, so this expansion could open up new possibilities in those areas.
Next Steps:
- Further Exploration: Further research is needed to explore the properties and potential applications of these generalized hypercomplex numbers and their associated algebras.
- Rigorous Evaluation: The mathematical community will need to carefully evaluate the proposed multiplication method and its implications.
- Interdisciplinary Collaboration: Collaborations between mathematicians, physicists, and engineers could help uncover new applications for these generalized number systems.
This is right up my alley in terms of research interests, but I’m not seeing the preprint anymore. I guess it was removed? How can I assist with this project?
Thank you for your interest. You can find preprint here: https://www.researchgate.net/publication/376201097_On_the_hypercomplex_numbers_and_normed_division_algebra_of_all_dimensions_A_unified_multiplication
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