Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T05:09:31.966Z Has data issue: false hasContentIssue false
  • English
  • Français

On Involutions of Quasi-Division Algebras

Published online by Cambridge University Press:  20 November 2018

Lowell Sweet
Lowell Sweet*
Affiliation:
University of Prince Edward Island, Charlottetown, P.E.I.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

All algebras are assumed to be finite dimensional and not necessarily associative. An involution of an algebra is an algebra automorphism of order two. A quasi-division algebra is any algebra in which the non-zero elements form a quasi-group under multiplication. The purpose of this short paper is to determine the structure of all involutions of quasi-division algebras and to give an application of this result.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 5 , February 1975 , pp. 723 - 725
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Djoković, D. Ž., Real homogeneous algebras, Proc. Amer. Math. Soc, 41 (1973), 457–462.Google Scholar
2. Feit, W. and Thompson, J., Solvability of groups of odd order, Pacific J. Math., 13 (1963), 775–1029.Google Scholar
3. Gross, F., Finite automorphic algebras over GF(2)9 Proc. Amer. Math. Soc, 4 (1971), 349- 353.Google Scholar
4. Kostrikin, A. I., On homogeneous algebras, Izvestia Acad. Nauk. U.S.S.R., 29 (1965), 471–484.Google Scholar