Lie-admissible algebra
From HandWiki
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 (3): 552–593, doi:10.2307/1990399, ISSN 0002-9947
- Hazewinkel, Michiel, ed. (2001), "Lie-admissible_algebra", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4, https://www.encyclopediaofmath.org/index.php?title=Lie-admissible_algebra
- Santilli, Ruggero Maria (1967), "Embedding of Lie-algebras into Lie-admissible algebras", Nuovo Cimento 51 (3): 570-585, ISSN 0002-9947, http://www.santilli-foundation.org/docs/Santilli-54.pdf
- Santilli, Ruggero Maria (1968), "An introduction to Lie-admissible algebras", Suppl. Nuovo Cimento 6 (1): 1225-1249, ISSN 0002-9947, http://www.santilli-foundation.org/docs/Santilli-501.pdf
- Myung, Hyo Chul (1986), Malcev-admissible algebras, Progress in Mathematics, 64, Boston, MA: Birkhäuser Boston, Inc., ISBN 0-8176-3345-6, https://books.google.com/books?id=PBvvAAAAMAAJ
- 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
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