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"quote": "\n\n> [!definition] 定义 · 李超代数\n>\n> 实或复向量空间 $V$ 上的[李超代数(Lie superalgebra)](../../../../../concepts/lie-theory/lie-superalgebra)结构由双线性映射[李超括号(Lie superbracket)](../../../../../concepts/lie-theory/lie-superbracket) $[\\cdot,\\cdot]_\\pm$ 给出。它在通常的或费米子的生成元 $X,Y,Z$ 上满足\n>\n> $$\n> [X,Y]_\\pm=-(-1)^{|X||Y|}[Y,X]_\\pm\n> $$\n>\n> 以及[超雅可比恒等式(super-Jacobi identity)](../../../../../concepts/lie-theory/super-jacobi-identity)\n>\n> $$\n> [X,[Y,Z]_\\pm]_\\pm=[[X,Y]_\\pm,Z]_\\pm+(-1)^{|X||Y|}[Y,[X,Z]_\\pm]_\\pm\n> $$\n>\n> 其中，通常生成元的 $|X|=0$，费米子生成元的 $|X|=1$。\n",
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