Category:Definitions/Lie Algebras
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This category contains definitions related to Lie Algebras.
Related results can be found in Category:Lie Algebras.
Let $L$ be an algebra over a ring.
Then $L$ is a Lie algebra if and only if it satisfies the Lie algebra axioms:
| \((\text L 0)\) | $:$ | Closure | \(\ds \forall a, b \in L:\) | \(\ds \sqbrk {a, b} \in L \) | |||||
| \((\text L 1)\) | $:$ | Alternativity | \(\ds \forall a \in L:\) | \(\ds \sqbrk {a, a} = 0 \) | |||||
| \((\text L 2)\) | $:$ | Jacobi Identity | \(\ds \forall a, b, c \in L:\) | \(\ds \sqbrk {a, \sqbrk {b, c} } + \sqbrk {b, \sqbrk {c, a} } + \sqbrk {c, \sqbrk {a, b} } = 0 \) |
where $\sqbrk {\, \cdot, \cdot \,}$ is the bilinear mapping on $L$.
Source of Name
This entry was named for Marius Sophus Lie.
Pages in category "Definitions/Lie Algebras"
The following 2 pages are in this category, out of 2 total.