Tagged Questions
2
votes
1answer
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Showing that the universal enveloping algebra of some $\mathfrak{g}$ is isomorphic to $\mathbb{C}[x_i,\partial/\partial x_i]$
The universal enveloping algebra $U(\mathfrak{g})$ of a Lie algebra $\mathfrak{g}$ over $\mathbb{C}$ is defined to be
$$
\dfrac{\mathbb{C}\oplus\mathfrak{g}\oplus ( \mathfrak{g}\otimes ...
1
vote
0answers
90 views
PBW Theorem applied to graded Lie algebras
Fix a $\mathbb Z_+^n$-graded Lie algebra ${\frak a}=\oplus_{r \in\mathbb Z_+^n}^{} {\frak a}[r]$ such that ${\frak g}:={\frak a}[0]$ is a finite-dimensional semisimple Lie algebra over the complex ...
3
votes
0answers
111 views
Integral forms of loop algebras.
The question following is about integral forms for semisimple Lie algebras and loop algebras constructed from them.
Let $\frak g$ a finite-dimensional Lie algebra over $\mathbb C$ and $L(\frak ...
