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Results tagged with lie-groups
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user 49781
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
2
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Reconstruction of a Poisson-Lie group structure from a Lie bialgebra $\mathfrak{g}$
Let $(\mathfrak{g}, [,], \delta)$ be a Lie bialgebra where $\delta$ is the cobracket. It is well-known that there exists a simply connected Poisson-Lie group $G$ such that $\mathfrak{g} = \mathrm{Lie} …
- 255
4
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Does a dual basis for $U_h(\mathfrak{sl}_2(\mathbb{C}))$ exist?
Let $\mathcal{F}_h(\operatorname{SL}_2(\mathbb{C}))$ be the $\mathbb{C}[[h]]$-algebra generated by $a, b, c, d$ subject to the following relations:
\begin{align*}
& ac = e^{-h}ca, \quad bd = e^{-h}db, …
- 255
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Concrete examples of quantum duality principle
Let $G$ be a Poisson Lie group, $\mathfrak{g}$ be a Lie algebra of $G$, $G^*$ be a dual of $G$, $\mathscr{C}(G^*)$ be a Poisson algebra of $G^*$, and $U_h(\mathfrak{g})$ be a quantized universal envel …
- 255