Abstract
Recall that an algebra (over the reals) is a real vector space A with a bilinear map A × A → A. This map can be thought of as a binary operation giving A a ring structure. We call A a Lie algebra if the binary operation, which we denote by [,], is anticommutative (that is, [a, b] = −[b,a]) and satisfies the Jacobi identity
We call [a, b] the commutator of a and b.
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© 1994 Springer-Verlag Berlin Heidelberg
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Schwarz, A.S. (1994). Lie Algebras. In: Topology for Physicists. Grundlehren der mathematischen Wissenschaften, vol 308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02998-5_14
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DOI: https://doi.org/10.1007/978-3-662-02998-5_14
Publisher Name: Springer, Berlin, Heidelberg
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