Euclidean group

但是通常余伴随作用必须被修正以使映射等价(this is the case for example for the Euclidean group). The modification is by a 1-cocycle on the group with values in g ∗ {\displaystyle {\mathfrak

常數向量只對繞其方向之軸的旋轉有旋轉對稱，及只有當其為零時才有反轉對稱。 一般對於在歐幾里得空間內對稱的觀念裡，G為歐幾里得群（英语：Euclidean group）E(n)，其為V為歐幾里得空間之等距同構的群。一物件的旋轉群為對稱群若G被侷限在direct

the perturbative theory. Under a Wick rotation, this is brought to a Euclidean metric G μ ν = δ μ ν {\displaystyle G_{\mu \nu }=\delta _{\mu \nu }}

Driessler, Fröhlich “The reconstruction of local observable algebras from the euclidean Green's functions of relativistic quantum field theory”, Annales de l'Institut

（原始内容存档于2017-03-14）.  Terras, Audrey. Harmonic Analysis on Symmetric Spaces-Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane 2nd. New York, NY: