论文标题
振荡器上的泊松代数和对称的莱布尼兹bialgebra结构。
Poisson algebras and symmetric Leibniz bialgebra structures on oscillator Lie algebras
论文作者
论文摘要
振荡器lie代数是唯一一个携带双重不变洛伦兹度量的非交换可解的代数。在本文中，我们确定了所有泊松结构，尤其是所有对称的Leibniz代数结构，其基本谎言代数为振荡器是代数。我们还提供了所有对称的Leibniz Bialgebra结构，其基本的谎言双子结构是振荡器的谎言bialgebra结构。我们对振荡器谎言组产生了一些几何后果。
Oscillator Lie algebras are the only non commutative solvable Lie algebras which carry a bi-invariant Lorentzian metric. In this paper, we determine all the Poisson structures, and in particular, all symmetric Leibniz algebra structures whose underlying Lie algebra is an oscillator Lie algebra. We give also all the symmetric Leibniz bialgebra structures whose underlying Lie bialgebra structure is a Lie bialgebra structure on an oscillator Lie algebra. We derive some geometric consequences on oscillator Lie groups.
