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Andrey Feldman
Andrey Feldman
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$sl(2,\mathbb{C})$$\mathfrak{sl}(2,\mathbb{C})$ is indeed equal to $sl(2,\mathbb{R}) \oplus sl(2,\mathbb{R})$$\mathfrak{sl}(2,\mathbb{R}) \oplus \mathfrak{sl}(2,\mathbb{R})$. The famous representation is given by $L_{-1}$, $L_0$, $L_1$ of the Virasoro algebra for the first copy of $sl(2, \mathbb{R})$$\mathfrak{sl}(2, \mathbb{R})$, and by their conjugations $\overline{L}_{-1}$, $\overline{L}_0$, $\overline{L}_1$ for the second one.

$sl(2,\mathbb{C})$ is indeed equal to $sl(2,\mathbb{R}) \oplus sl(2,\mathbb{R})$. The famous representation is given by $L_{-1}$, $L_0$, $L_1$ of the Virasoro algebra for the first copy of $sl(2, \mathbb{R})$, and by their conjugations $\overline{L}_{-1}$, $\overline{L}_0$, $\overline{L}_1$ for the second one.

$\mathfrak{sl}(2,\mathbb{C})$ is indeed equal to $\mathfrak{sl}(2,\mathbb{R}) \oplus \mathfrak{sl}(2,\mathbb{R})$. The famous representation is given by $L_{-1}$, $L_0$, $L_1$ of the Virasoro algebra for the first copy of $\mathfrak{sl}(2, \mathbb{R})$, and by their conjugations $\overline{L}_{-1}$, $\overline{L}_0$, $\overline{L}_1$ for the second one.

Source Link
Andrey Feldman
Andrey Feldman
  • 2k
  • 1
  • 11
  • 24

$sl(2,\mathbb{C})$ is indeed equal to $sl(2,\mathbb{R}) \oplus sl(2,\mathbb{R})$. The famous representation is given by $L_{-1}$, $L_0$, $L_1$ of the Virasoro algebra for the first copy of $sl(2, \mathbb{R})$, and by their conjugations $\overline{L}_{-1}$, $\overline{L}_0$, $\overline{L}_1$ for the second one.