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, Lie algebras, and Okubo algebras.

See also

• Malcev-admissible algebra
• Jordan-admissible algebra

References

• 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