Complete left-invariant affine structures on nilpotent Lie groups
From MaRDI portal
Publication:1074876
DOI10.4310/jdg/1214440553zbMath0591.53045OpenAlexW1544626381WikidataQ115185021 ScholiaQ115185021MaRDI QIDQ1074876
Publication date: 1986
Published in: Journal of Differential Geometry (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4310/jdg/1214440553
left-symmetric algebrapseudo-Riemannian structuresaffine manifoldsflat structuresleft-invariant affine structuresimply connected Lie groups
Differential geometry of homogeneous manifolds (53C30) Nilpotent and solvable Lie groups (22E25) Linear and affine connections (53B05)
Related Items (63)
Simply transitive nil-affine actions of solvable Lie groups ⋮ The construction and deformation of Novikov H-pseudoalgebras ⋮ Left-symmetric algebras from linear functions ⋮ Left-symmetric bialgebroids and their corresponding Manin triples ⋮ Commutative post-Lie algebra structures on Lie algebras ⋮ Novikov-Poisson algebras ⋮ Modules for certain Lie algebras of maximal class ⋮ Affine structures on 4-step nilpotent Lie algebras ⋮ The five-dimensional complete left-symmetric algebra structures compatible with an abelian Lie algebra structure ⋮ On bi-symmetric algebras ⋮ A Zassenhaus conjecture and CPA-structures on simple modular Lie algebras ⋮ Expanding maps, Anosov diffeomorphisms and affine structures on infra-nilmanifolds. ⋮ Left-symmetric superalgebra structures on the super Galilean conformal algebra ⋮ A left-symmetric algebraic approach to left invariant flat (pseudo-)metrics on Lie groups ⋮ Hopf braces and Yang-Baxter operators ⋮ Central Extensions and Hom-Quadratic Hom-Novikov Color Algebras ⋮ LEFT-SYMMETRIC BIALGEBRAS AND AN ANALOGUE OF THE CLASSICAL YANG–BAXTER EQUATION ⋮ Left-symmetric algebra structures on the \(W\)-algebra \(W(2, 2)\) ⋮ On a class of Lie groups with a left invariant flat pseudo-metric ⋮ Translations in simply transitive affine actions of 5-dimensional nilpotent Lie groups. ⋮ Novikov algebras carrying an invariant Lorentzian symmetric bilinear form ⋮ Left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra ⋮ Commutative post-Lie algebra structures and linear equations for nilpotent Lie algebras ⋮ Left-symmetric algebras, or pre-Lie algebras in geometry and physics ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Extending structures and classifying complements for left-symmetric algebras ⋮ KV-COHOMOLOGY OF KOSZUL–VINBERG ALGEBROIDS AND POISSON MANIFOLDS ⋮ Pre-symplectic algebroids and their applications ⋮ Non-associative structures of commutative algebras related with quadratic Poisson brackets ⋮ Weighted infinitesimal unitary bialgebras on free monoid algebras ⋮ Left-symmetric algebras and homogeneous improper affine spheres ⋮ Classification of derivation algebras in low dimensions ⋮ The structure of assosymmetric algebras ⋮ Some non-abelian phase spaces in low dimensions ⋮ Abelian Hessian algebra and commutative Frobenius algebra ⋮ The structure of complete left-symmetric algebras ⋮ Kaehlerian reductions in solvable Lie groups and applications ⋮ Construction of finite braces ⋮ Hom Gel'fand-Dorfman bialgebras and Hom-Lie conformal algebras ⋮ Nilpotent Lie groups admitting a left invariant structure ⋮ Post-Lie algebra structures for nilpotent Lie algebras ⋮ Classification of simple Novikov algebras and their irreducible modules of characteristic 0 ⋮ The Riccati and Ermakov-Pinney hierarchies ⋮ COHOMOLOGY AND HOMOLOGY OF ABELIAN GROUPS GRADED KOSZUL–VINBERG ALGEBRAS ⋮ Projective non affine structures on filiform Lie groups ⋮ Rota–Baxter operators and post-Lie algebra structures on semisimple Lie algebras ⋮ Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems ⋮ Weighted infinitesimal unitary bialgebras, pre-Lie, matrix algebras, and polynomial algebras ⋮ Commutative post-Lie algebra structures on Kac–Moody algebras ⋮ A FURTHER STUDY ON NON-ABELIAN PHASE SPACES: LEFT-SYMMETRIC ALGEBRAIC APPROACH AND RELATED GEOMETRY ⋮ Affine structures on a class of virtually nilpotent groups ⋮ Cohomologies and deformations of right-symmetric algebras ⋮ Commutative post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras ⋮ Quadratic conformal superalgebras ⋮ Reduced pre-Lie algebraic structures, the weak and weakly deformed Balinsky-Novikov type symmetry algebras and related Hamiltonian operators ⋮ On the number of abelian left symmetric algebras ⋮ Affine structures on abelian Lie groups ⋮ On the Novikov algebra structures adapted to the automorphism structure of a Lie group. ⋮ A Lie algebraic approach to Novikov algebras. ⋮ Translations in simply transitive affine actions of Heisenberg type Lie groups ⋮ Soliton almost Kähler structures on 6-dimensional nilmanifolds for the symplectic curvature flow ⋮ Left-symmetric algebras for 𝔤𝔩(𝔫)
This page was built for publication: Complete left-invariant affine structures on nilpotent Lie groups