Last Updated
：2025/12/03
Jacobi identity
Noun
countable
uncountable
Japanese Meaning
数学において、加算演算および加算単位元を持つ集合 S 上で定義された二項演算 × に対し、任意の元 a, b, c ∈ S について a × (b×c) + b × (c×a) + c × (a×b) = 0 となる性質（ジャコビ恒等式）を意味する。
（ plural ）
Quizzes for review
(mathematics) Given a binary operation × defined on a set S which also has additive operation + and additive identity 0, the property that a × (b×c) + b × (c×a) + c × (a×b) = 0 for all a, b, c in S.
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Jacobi identity
In many Lie algebra proofs, the Jacobi identity ensures that the cyclic sum a × (b×c) + b × (c×a) + c × (a×b) vanishes.
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In many Lie algebra proofs, the Jacobi identity ensures that the cyclic sum a × (b×c) + b × (c×a) + c × (a×b) vanishes.
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