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Lie Algebra

A Nonassociative Algebra obeyed by objects such as the Lie Bracket and Poisson Bracket. Elements $f$, $g$, and $h$ of a Lie algebra satisfy

\end{displaymath} (1)

\end{displaymath} (2)

\end{displaymath} (3)

(the Jacobi Identity), and are not Associative. The binary operation of a Lie algebra is the bracket
\end{displaymath} (4)

See also Jacobi Identities, Lie Algebroid, Lie Bracket, Iwasawa's Theorem, Poisson Bracket


Lie Algebra

Jacobson, N. Lie Algebras. New York: Dover, 1979.

© 1996-9 Eric W. Weisstein