论文标题
谎言代数卡罗尔/伽利利二重性
Lie algebraic Carroll/Galilei duality
论文作者
论文摘要
我们表征了谎言群体与双不可变化的Bargmannian，Galilean或Carrollian结构。我们在身份定位时表明，具有广告不变的Bargmannian，Carrollian或Galilean结构的代数实际上是由相同的数据确定的：具有偏度对称派生的度量代数。这是定义公制谎言代数的一维双重扩展的相同数据，实际上，Bargmannian Lie代数与此类双重扩展相吻合，其中包含Carrollian Lie代数为理想，并投影了Galilean Lie lie代数。这建立了由Bargmannian Lie代数介导的Carrollian和Galilean Lie代数之间的规范对应关系。这种重新制定使我们能够利用公制谎言代数的结构理论在积极的案例中列出了Bargmannian，Carrollian和Galilean Lie代数的列表。我们还表征了承认双重不变（环境）莱布尼兹结构的谎言群体。 Leibnizian Lie代数扩展了Bargmannian Lie代数的类别，并在Carrollian和Galilean Lie代数之间建立了非典型的对应关系。
We characterise Lie groups with bi-invariant bargmannian, galilean or carrollian structures. Localising at the identity, we show that Lie algebras with ad-invariant bargmannian, carrollian or galilean structures are actually determined by the same data: a metric Lie algebra with a skew-symmetric derivation. This is the same data defining a one-dimensional double extension of the metric Lie algebra and, indeed, bargmannian Lie algebras coincide with such double extensions, containing carrollian Lie algebras as an ideal and projecting to galilean Lie algebras. This sets up a canonical correspondence between carrollian and galilean Lie algebras mediated by bargmannian Lie algebras. This reformulation allows us to use the structure theory of metric Lie algebras to give a list of bargmannian, carrollian and galilean Lie algebras in the positive-semidefinite case. We also characterise Lie groups admitting a bi-invariant (ambient) leibnizian structure. Leibnizian Lie algebras extend the class of bargmannian Lie algebras and also set up a non-canonical correspondence between carrollian and galilean Lie algebras.
