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Connections and Finsler geometry of the structure group of a JB-algebra by Larotonda, Gabriel; Luna, José is a scholarly article available to read on EtoBox.

What is Connections and Finsler geometry of the structure group of a JB-algebra about?

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 $G(\Omega)$, the group of transformations that preserve the positive cone $\Omega$ of the algebra $V$, and to $Aut(V)$, the group of Jordan automorphisms of the algebra. We present the cone $\Omega$ as an homogeneous space for the action of $G(\Omega)$, therefore inducing a quotient Finsler metric and distance. With the techniques introduced, we prove the minimality of the one-parameter groups in $\Omega$ for any symmetric gauge norm in $V$. We establish that the two presentations of the Finsler metric in $\Omega$ give the same distance there, which helps us prove the minimality of certain paths in $G(\Omega)$ for its left-invariant Finsler metric.

Author

Larotonda, Gabriel; Luna, José

Published

2022

Language

EN