论文标题
LIFSHITZ对称：谎言代数，空间和颗粒
Lifshitz symmetry: Lie algebras, spacetimes and particles
论文作者
论文摘要
我们研究并分类由空间旋转，时间和空间翻译以及附加标量发生器产生的谎言组的均匀空间和coadhexhexhexightime和coadhexhexhexhexightime和coadhexhexhexhechoint Orbits（“颗粒”）。作为第一步，我们将这种类型的代数分类为任意维度。其中包括典型的Lifshitz代数，它激发了这项工作和“ Lifshitz Lie代数”的名称。我们将Lifshitz Lie组的均匀时间进行分类。根据对其他标量发生器的解释，这些空间分为三个类： （1）（$ d+2 $） - 尺寸LIFSHITZ SPACETIMER，它具有另一个全息方向； （2）（$ d+1 $） - 尺寸lifshitz-weyl空间，可以看作是（1）中空间的边界几何形状，而标量发生器被解释为各向异性扩张；和 （3）（$ d+1 $） - 一个标量电荷的尺寸亚里士多德空间，包括概括多极代代数的异国情调的类似的符号。 我们还对Lifshitz Lie代数的可能中心扩展进行了分类，并讨论了Lifshitz Lie组的同质象征性歧管，该歧管属于Coadchoint Orbits。
We study and classify Lie algebras, homogeneous spacetimes and coadjoint orbits ("particles") of Lie groups generated by spatial rotations, temporal and spatial translations and an additional scalar generator. As a first step we classify Lie algebras of this type in arbitrary dimension. Among them is the prototypical Lifshitz algebra, which motivates this work and the name "Lifshitz Lie algebras". We classify homogeneous spacetimes of Lifshitz Lie groups. Depending on the interpretation of the additional scalar generator, these spacetimes fall into three classes: (1) ($d+2$)-dimensional Lifshitz spacetimes which have one additional holographic direction; (2) ($d+1$)-dimensional Lifshitz--Weyl spacetimes which can be seen as the boundary geometry of the spacetimes in (1) and where the scalar generator is interpreted as an anisotropic dilation; and (3) ($d+1$)-dimensional aristotelian spacetimes with one scalar charge, including exotic fracton-like symmetries that generalise multipole algebras. We also classify the possible central extensions of Lifshitz Lie algebras and we discuss the homogeneous symplectic manifolds of Lifshitz Lie groups in terms of coadjoint orbits.
