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--- commutator_relations [2023/06/07 13:54] – [Connections] spencer
+++ commutator_relations [2023/06/07 13:55] (current) – spencer
@@ Line 3: / Line 3: @@
 ==== Exterior and Interior products ====
- - For forms $\alpha, \beta$, $e^*(\alpha)e(\beta) = e(e^*(\alpha)\beta) + (-1)^{|\alpha|} e(\beta) e^*(\alpha)$. Using $[x, y]_g$ for the graded commutator $xy - (-1)^{|x|}yx$, then $[e^*(\alpha), e(\beta)]_g = e(e^*(\alpha)\beta)$. In particular, for the 1-forms $\omega^i$ we have $e^*(\omega^i) e(\omega^j) + e(\omega^j) e^*(\omega^i) = 0$ for $i \neq j$, and is the identity otherwise.
+    - For forms $\alpha, \beta$, $e^*(\alpha)e(\beta) = e(e^*(\alpha)\beta) + (-1)^{|\alpha|} e(\beta) e^*(\alpha)$. Using $[x, y]_g$ for the graded commutator $xy - (-1)^{|x|}yx$, then $[e^*(\alpha), e(\beta)]_g = e(e^*(\alpha)\beta)$. In particular, for the 1-forms $\omega^i$ we have $e^*(\omega^i) e(\omega^j) + e(\omega^j) e^*(\omega^i) = 0$ for $i \neq j$, and is the identity otherwise.
 ==== Connections ====