# Connections and Finsler geometry of the structure group of a JB-algebra

@inproceedings{Larotonda2022ConnectionsAF, title={Connections and Finsler geometry of the structure group of a JB-algebra}, author={Gabriel Larotonda and Jos'e Luna}, year={2022} }

. 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…

## One Citation

### On the structure group of an infinite dimensional JB-algebra

- Mathematics
- 2022

. We extend several results for the structure group of a real Jordan algebra V , to the setting of inﬁnite dimensional JB-algebras. We prove that the structure group Str ( V ), the cone preserving…

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