Open AccessMultenions and differential invariants
Author(s) -
Alex McAulay
Publication year - 1921
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1921.0044
Subject(s) - quaternion , algebra over a field , differential (mechanical device) , differential geometry , mathematics , subject (documents) , development (topology) , pure mathematics , computer science , calculus (dental) , mathematical analysis , physics , geometry , medicine , dentistry , library science , thermodynamics
1.Preliminary Explanations .—Since multenions appear almost to have been designed by Nature to serve as an algebra dealing with such matters as differential invariants and relativity, I have thought it desirable at the present moment to present a summary of their properties. Towards the end I propose to enter into more detail in applying them to differential invariants, and to point out some of the special properties of multenions whenn , the vector complexity of the system, has the particular value 4. Clifford first, I believe, applied the subject to elliptic space of three dimensions. His bi-quaternionq +ωr , whereω 2 = 1, is the general member of a sub-algebra of multenions whenn = 4. In the form of multenions suitable to deal with real questions of Relativity Hamilton’s bi-quaternionq +r √(—1) presents itself in a precisely similar manner, and of this I shall have more to say towards the end of the paper. Joly’s ‘Manual of Quaternions’ has its last chapter devoted wholly to multenions. I believe the most elaborate attempt at development is my own paper in ‘Proc. Roy. Soe., Edin.,’ 1907-8, p. 503.