Lie-admissible algebra
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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
[edit]References
[edit]- ^ 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, JSTOR 1990399, MR 0027750
- "Lie-admissible_algebra", Encyclopedia of Mathematics, EMS Press, 2001 [1994]
- Santilli, Ruggero Maria (1967), "Embedding of Lie-algebras into Lie-admissible algebras" (PDF), Nuovo Cimento, 51 (3): 570–585, ISSN 0002-9947, JSTOR 1990399, MR 0027750
- Santilli, Ruggero Maria (1968), "An introduction to Lie-admissible algebras" (PDF), Suppl. Nuovo Cimento, 6 (1): 1225–1249, ISSN 0002-9947, JSTOR 1990399, MR 0027750
- Myung, Hyo Chul (1986), Malcev-admissible algebras, Progress in Mathematics, vol. 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, vol. 2, Cambridge: Cambridge University Press, p. 22, ISBN 0-521-47215-6, Zbl 0841.17001
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