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Results tagged with dg.differential-geometry
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user 11877
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
1
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130
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Lie algebra action obtained from Lie group action [closed]
Suppose that $G, H$ are Lie groups and $\mathfrak{g}$ the Lie algebra of $G$. Suppose that there is a Lie group action $G \times H \to H$. Is there a natural $\mathfrak{g}$ action on $C^{\infty}(H)$? …
- 6,201
2
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1
answer
241
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Trying to understand dressing actions
I am reading the lecture notes and trying to understand dressing actions.
Let $G$ be a Poisson-Lie group and $G^*$ its dual Poisson-Lie group. In the lecture notes above, Proposition 5.22 on page 80 …
- 6,201
1
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0
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73
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Decompose elements in $SL_2$ as a pair of elements in $SL_2^*$.
I have a question about decomposing elements in $SL_2$ as a pair of elements in $SL_2^*$. Here $SL_2^*$ is the dual Poisson Lie group of $SL_2$ which is defined as follows.
Let $G$ be a Poisson-Lie …
- 6,201
1
vote
1
answer
93
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How to show that the structure constant on $\mathcal{G}^*$ is $C_{c}^{ab} = f_{cd}^b r^{ad} ...
Let $(\mathcal{G}, \mathcal{G}^*, \delta)$ be a Lie bialgebra. Suppose that the structure constant on $\mathcal{G}^*$ and $\mathcal{G}$ are
\begin{align}
& [t^a, t^b]_* = C_c^{ab} t_c, \\
& [t_a, t_b] …
- 6,201