Finite generation of Lie algebras of Poisson brackets. (English) Zbl 1514.17024
Summary: Let \(L\) be a finite dimensional Lie algebra. Let \(U(L)\) and \(\mathrm{Pol}(L)\) be the universal enveloping algebra of \(L\) and the related Poisson algebra. We find conditions for finite generation of Lie algebras \([U(L),U(L)]\) and \([\mathrm{Pol}(L), \mathrm{Pol}(L)]\).
MSC:
| 17B60 | Lie (super)algebras associated with other structures (associative, Jordan, etc.) |
| 17B63 | Poisson algebras |
| 17B35 | Universal enveloping (super)algebras |
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