论文标题
与振荡器代数有关的指标
Metrics related to Oscillator algebras
论文作者
论文摘要
如果谎言代数允许对称不变且非排定双线性形式，则是公制的。谐波振荡器代数是在谐波振荡器的量子机械描述中产生的，是最小的可溶解的非阿布尔度量示例。该代数是一系列可计数可解的谎言代数的第一步，该代数支持不变的洛伦兹形式。概括这种情况，在本文中，我们到达振荡器作为度量空间的双重扩展。本文的目的是介绍此类代数的一些结构特征，不变的指标和推导，并探索它们扩展到混合度量代数代数的可能性。
A Lie algebra is said to be metric if it admits a symmetric invariant and nondegenerate bilinear form. The harmonic oscillator algebra, which arises in the quantum mechanical description of a harmonic oscillator, is the smallest solvable nonabelian metric example. This algebra is the first step of a countable series of solvable Lie algebras which support invariant Lorentzian forms. Generalizing this situation, in this paper we arrive to the oscillator Lie K-algebras as double extensions of metric spaces. The aim of this paper is to present some structural features, invariant metrics and derivations of this class of algebras and to explore their possibilities of being extended to mixed metric Lie algebras.
