Lie- algebra

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In mathematics, a Lie-* algebra is a D-module with a Lie* bracket. They were introduced by Alexander Beilinson and Vladimir Drinfeld ((Beilinson Drinfeld)), and are similar to the conformal algebras discussed by (Kac 1998) and to vertex Lie algebras.

## References

* Beilinson, Alexander; Drinfeld, Vladimir (2004), Chiral algebras, American Mathematical Society Colloquium Publications, 51, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-3528-9, https://books.google.com/books?id=yHZh3p-kFqQC
* Kac, Victor (1998), Vertex algebras for beginners, University Lecture Series, 10 (2nd ed.), Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1396-6, https://books.google.com/books?id=PIhm9-37IlUC

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

1. ↑ 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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