National University of General Sarmiento

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20022014

most citedNichols algebras of group type with many quadratic relations

50 citations

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math.DG2011★ 2 cited

Optimal paths for symmetric actions in the unitary group

Jorge Antezana, Gabriel Larotonda, Alejandro Varela

Given a positive and unitarily invariant Lagrangian L defined in the algebra of Hermitian matrices, and a fixed interval $[a, b] \subset R$ , we study the action defined in the…

math.DG2008

Weak Riemannian manifolds from finite index subfactors

Esteban Andruchow, Gabriel Larotonda

Let $N \subset M$ be a finite Jones' index inclusion of II $_{1}$ factors, and denote by $U_{N} \subset U_{M}$ their unitary groups. In this paper we study the homogeneous space $U_{M} / U_{N}$ ,…

math.DG2008★ 1 cited

Hopf-Rinow Theorem in the Sato Grassmannian

Esteban Andruchow, Gabriel Larotonda

Let $U_{2} (H)$ be the Banach-Lie group of unitary operators in the Hilbert space $H$ which are Hilbert-Schmidt perturbations of the identity 1. In this paper we study t…

math.DG2008★ 8 cited

Lagrangian Grassmannian in Infinite Dimension

Esteban Andruchow, Gabriel Larotonda

Given a complex structure $J$ on a real (finite or infinite dimensional) Hilbert space $H$ , we study the geometry of the Lagrangian Grassmannian $Λ (H)$ of $H$ , i.e. the set of clos…

math.DG2008

Nonpositively curved metric in the positive cone of a finite von Neumann algebra

Esteban Andruchow, Gabriel Larotonda

In this paper we study the metric geometry of the space $Σ$ of positive invertible elements of a von Neumann algebra $A$ with a finite, normal and faithful tracial state…

math.DG2008

Unitary orbits in a full matrix algebra

Gabriel Larotonda

The Hilbert manifold $Σ$ consisting of positive invertible (unitized) Hilbert-Schmidt operators has a rich structure and geometry. The geometry of unitary orbits $Ω \subset Σ$ is st…