• Corpus ID: 249889787

# 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}
}
• Published 18 June 2022
• Mathematics
. 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…
1 Citations

### 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

## References

SHOWING 1-10 OF 41 REFERENCES

### 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

### Metric geometry of infinite-dimensional Lie groups and their homogeneous spaces

Abstract We study the geometry of Lie groups G with a continuous Finsler metric, in presence of a subgroup K such that the metric is right-invariant for the action of K. We present a systematic study

### Metric convexity of symmetric cones

• Mathematics
• 2007
AbstractIn this paper we introduce a general notion of a symmetric cone, valid for theﬁnite and inﬁnite dimensional case, and prove that one can de duce the seminegativecurvature of the Thompson part

### GEODESICS AND OPERATOR MEANS IN THE SPACE OF POSITIVE OPERATORS

• Mathematics
• 1993
The set A+ of positive invertible elements of a C*-algebra has a natural structure of reductive homogeneous manifold with a Finsler metric. Because pairs of points can be joined by uniquely

### Hilbert and Thompson isometries on cones in JB-algebras

• Mathematics
Mathematische Zeitschrift
• 2018
Hilbert’s and Thompson’s metric spaces on the interior of cones in JB-algebras are important examples of symmetric Banach-Finsler spaces. In this paper we characterize the Hilbert’s metric isometries

### A Cartan–Hadamard Theorem for Banach–Finsler Manifolds

In this paper we study Banach–Finsler manifolds endowed with a spray which have seminegative curvature in the sense that the corresponding exponential function has a surjective expansive differential

### Differential Geometry for Nuclear Positive Operators

Abstract.Let H be a Hilbert space, $$\dim H = \infty$$ . The set Δ1 = {1 + a : a in the trace class, 1 + a positive and invertible} is a differentiable manifold of operators, and a homogeneous

### Siegel domains over Finsler symmetric cones

Abstract Let Ω be a proper open cone in a real Banach space V. We show that the tube domain V⊕i⁢Ω{V\oplus i\Omega} over Ω is biholomorphic to a bounded symmetric domain if and only if Ω is a normal