论文标题
JB-Elgebra结构组的连接和鳍的几何形状
Connections and Finsler geometry of the structure group of a JB-algebra
论文作者
论文摘要
我们通过左右连接和Finsler指标赋予无限尺寸JB-Algebra $ V $的Banach-Lie结构组$ str（V）$，我们计算了其所有数量的连接。我们展示了这种连接如何减少到$ g（ω）$，即代数$ v $的正锥$ω$的一组转换，以及$ aut（v）$，即代数的约旦自动形态。我们将锥体$ω$作为$ g（ω）$的动作的均匀空间，因此引起了商标的鳍量和距离。通过引入这些技术，我们证明，对于$ v $的任何对称量规标准，单参数群以$ω$中的$ω$中的最低限制。我们确定$ω$的Finsler指标的两个演示文稿在那里给出了相同的距离，这有助于我们证明其剩余不变的Finsler Metric的$ g（ω）$中某些路径的最小值。
We endow the Banach-Lie structure group $Str(V)$ of an infinite dimensional JB-algebra $V$ with a left-invariant connection and Finsler metric, and we compute all the quantities of its connection. We show how this connection reduces to $G(Ω)$, the group of transformations that preserve the positive cone $Ω$ of the algebra $V$, and to $Aut(V)$, the group of Jordan automorphisms of the algebra. We present the cone $Ω$ as an homogeneous space for the action of $G(Ω)$, therefore inducing a quotient Finsler metric and distance. With the techniques introduced, we prove the minimality of the one-parameter groups in $Ω$ for any symmetric gauge norm in $V$. We establish that the two presentations of the Finsler metric in $Ω$ give the same distance there, which helps us prove the minimality of certain paths in $G(Ω)$ for its left-invariant Finsler metric.
