TWO-STEP NILPOTENT LIE ALGEBRAS WITH AD-INVARIANT METRICS AND A SPECIAL KIND OF SKEW-SYMMETRIC MAPS

DOI10.1142/S0219498807002557zbMath1205.17014arXivmath/0611789WikidataQ115245708 ScholiaQ115245708MaRDI QIDQ5386935

Gabriela Paola Ovando

Publication date: 14 May 2008

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611789

zbMATH Keywords

2-step nilpotent Lie algebrasclassical r-matrixcompact Lie algebrasAd-invariant metrics

Mathematics Subject Classification ID

Lie algebras of Lie groups (22E60) Solvable, nilpotent (super)algebras (17B30)

Related Items

Nearly para-Kähler geometry on Lie groups ⋮ Two-step nilpotent quadratic Lie algebras and 8-dimensional non-commutative symmetric Novikov algebras ⋮ New pseudo Einstein metrics on Einstein solvmanifolds ⋮ Quadratic 2-step Lie algebras: computational algorithms and classification ⋮ Free nilpotent Lie algebras admitting ad-invariant metrics ⋮ Sectional nonassociativity of metrized algebras ⋮ Invariant metrics on central extensions of quadratic Lie algebras ⋮ Double extensions on Riemannian Ricci nilsolitons ⋮ Free nilpotent and nilpotent quadratic Lie algebras ⋮ Pseudo-Riemannian Einstein metrics on noncompact homogeneous spaces

Cites Work

• The local structure of Poisson manifolds
• What is a classical r-matrix?
• Groupes de Lie munis de métriques bi-invariantes. (Lie groups admitting bi-invariant metrics)
• Symmetric, invariant, non-degenerate bilinear form on a Lie algebra
• Homogeneous nilmanifolds attached to representations of compact Lie groups
• Poisson structures on double Lie groups
• Geometry of $2$-step nilpotent groups with a left invariant metric
• Poisson-Lie \(T\)-duality