Hostname: page-component-84b7d79bbc-g5fl4 Total loading time: 0 Render date: 2024-07-29T03:23:54.460Z Has data issue: false hasContentIssue false
  • English
  • Français

On Anti-Commutative Algebras with an Invariant Form

Published online by Cambridge University Press:  20 November 2018

Arthur A. Sagle
Arthur A. Sagle*
Affiliation:
Syracuse University
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.

In this paper we consider anti-commutative algebras with an invariant form, that is, an algebra A over a field F such that

and A possesses a symmetric bilinear form f(x, y) such that

Lie and Malcev algebras (2, 3) are examples of such algebras and we shall consider generalizations of these algebras obtained by introducing commutation, x o y = xy — yx, as a new multiplicative operation in the non-commutative Jordan algebras of (1).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 370 - 378
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Paige, L. J., A note on noncommutative Jordan algebras, Portugal. Math., 16 (1957), 15–18.Google Scholar
2. Sagle, A. A., Malcev algebras, Trans. Amer. Math. Soc, 101 (1961), 426–458.Google Scholar
3. Sagle, A. A., On simple Malcev algebras over fields of characteristic zero, Pacific J. Math. 12 (1962), 1057–1078.Google Scholar
4. Schafer, R. D., On the algebras formed by the Cayley-Dickson process, Amer. J. Math., 76 (1954), 435–446.Google Scholar