Lie-admissible algebra
In algebra, a Lie-admissible algebra, introduced by A. Adrian Albert (1948), is a (possibly non-associative) algebra that becomes a Lie algebra under the bracket [a,b] = ab–ba. Examples include associative algebras,[1] Lie algebras, and Okubo algebras.
See also
- Malcev-admissible algebra
- Jordan-admissible algebra
References
- Okubo 1995, p. 19
- Albert, A. Adrian (1948), "Power-associative rings", Transactions of the American Mathematical Society, 64: 552–593, doi:10.2307/1990399, ISSN 0002-9947, JSTOR 1990399, MR 0027750
- Hazewinkel, Michiel, ed. (2001) [1994], "Lie-admissible_algebra", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
- Myung, Hyo Chul (1986), Malcev-admissible algebras, Progress in Mathematics, 64, Boston, MA: Birkhäuser Boston, Inc., ISBN 0-8176-3345-6, MR 0885089
- Okubo, Susumu (1995), Introduction to octonion and other non-associative algebras in physics, Montroll Memorial Lecture Series in Mathematical Physics, 2, Cambridge: Cambridge University Press, p. 22, ISBN 0-521-47215-6, Zbl 0841.17001CS1 maint: ref=harv (link)
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.