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Results tagged with lie-algebra-cohomology
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user 122414
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Calculation of Dynkin operator on free Lie rings
Let $A$ be a free associative ${\mathbb Z}$-algebra on generators $I = \{ x_i ~:~ I \in {\mathbb N} \}$. Setting the usual bracket $[a,b] = ab-ba$, it forms a free Lie ring $A^{(-)}$. The Dynkin opera …
- 405
1
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Calculation of Dynkin operator on free Lie rings
Lemma : If $\delta$ is the Dynkin operator defined as above, then
$$
\delta(x_{k+l} x_{k+l-1} \dotsc x_{k+1} [x_1, \dotsc, x_k]) = \left[ [x_{k+l}, x_{k+l-1}, \dotsc, x_{k+1}], [x_1, \dotsc, x_k] \ri …
- 405