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] Okubo algebras .
See also
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 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
