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        "quote": "注意，这些对易关系与李代数 $\\mathfrak{su}(2)$ 的基向量 $X_1,X_2,X_3$ 所满足的[方程 3.5](../chapter-03/02-commutation-relations-for-pauli-matrices#equation-3-5) 完全相同，因此 $\\mathfrak{so}(3)$ 与 $\\mathfrak{su}(2)$ 是同构的李代数。二者都是带有相同[<u id=\"concept-6-lie-bracket\" class=\"concept-term\" data-concept-reference=\"concepts/lie-theory/lie-bracket\" data-concept-id=\"concept-6-lie-bracket\" data-concept-identity=\"urn:uuid:2ec20f01-7d55-4d42-bfe7-cf436d149036\" data-concept-route=\"/concept-identities#concept-2ec20f01-7d55-4d42-bfe7-cf436d149036\">李括号(Lie bracket)</u>](../../../../../concepts/lie-theory/lie-bracket)运算的[<u id=\"concept-6-vector-space\" class=\"concept-term\" data-concept-reference=\"concepts/linear-algebra/vector-space\" data-concept-id=\"concept-6-vector-space\" data-concept-identity=\"urn:uuid:54e19cc9-1e38-4128-acaa-80499dfd908c\" data-concept-route=\"/concept-identities#concept-54e19cc9-1e38-4128-acaa-80499dfd908c\">向量空间(vector space)</u>](../../../../../concepts/linear-algebra/vector-space) $\\mathbf R^3$。这种运算在另一语境中也很熟悉：它就是标准基向量的[<u id=\"concept-6-cross-product\" class=\"concept-term\" data-concept-reference=\"concepts/linear-algebra/vector-cross-product\" data-concept-id=\"concept-6-cross-product\" data-concept-identity=\"urn:uuid:9217da23-ed1d-4016-b7e9-9a1d7c04a546\" data-concept-route=\"/concept-identities#concept-9217da23-ed1d-4016-b7e9-9a1d7c04a546\">叉积(cross product)</u>](../../../../../concepts/linear-algebra/vector-cross-product)：",
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