• Publications
  • Influence
Left-symmetric algebras, or pre-Lie algebras in geometry and physics
  • D. Burde
  • Physics, Mathematics
  • 10 September 2005
In this survey article we discuss the origin, theory and applications of left-symmetric algebras (LSAs in short) in geometry in physics. Recently Connes, Kreimer and Kontsevich have introduced LSAsExpand
  • 178
  • 11
  • PDF
Classification of Orbit Closures of 4-Dimensional Complex Lie Algebras
Abstract Let L n( C ) be the variety of complexn-dimensional Lie algebras. The groupGLn( C ) acts on it via change of basis. An orbitO(μ) under this action consists of all structures isomorphic to μ.Expand
  • 101
  • 9
  • PDF
On a refinement of Ado's theorem
Abstract. In this paper we study the minimal dimension $ \mu (g) $ of a faithful g-module for n-dimensional Lie algebras g. This is an interesting invariant of g which is difficult to compute. It isExpand
  • 45
  • 8
  • PDF
DEGENERATIONS OF 7-DIMENSIONAL NILPOTENT LIE ALGEBRAS
ABSTRACT We study the varieties of Lie algebra laws and their subvarieties of nilpotent Lie algebra laws. We classify all degenerations of (almost all) five-step and six-step nilpotentExpand
  • 48
  • 7
  • PDF
Simple left-symmetric algebras with¶solvable Lie algebra
Abstract:Left-symmetric algebras (LSAs) are Lie admissible algebras arising from geometry. The leftinvariant affine structures on a Lie group {G} correspond bijectively to LSA-structures on its LieExpand
  • 63
  • 6
  • PDF
Degenerations of nilpotent Lie algebras
In this paper we study degenerations of nilpotent Lie algebras. If ; are two points in the variety of nilpotent Lie algebras, then is said to degenerate to , !deg , if lies in the Zariski closure ofExpand
  • 33
  • 3
AFFINE STRUCTURES ON NILMANIFOLDS
We investigate the existence of affine structures on nilmanifolds Γ\G in the case where the Lie algebra g of the Lie group G is filiform nilpotent of dimension less or equal to 11. Here we obtainExpand
  • 86
  • 2
  • PDF
Left-Invariant Affine Structures on Reductive Lie Groups
We describe left-invariant affine structures (that is, left-invariant flat torsion-free affine connections ∇) on reductive linear Lie groupsG. They correspond bijectively to LSA-structures on the LieExpand
  • 39
  • 2
  • PDF
Left-invariant affine structures on nilpotent Lie groups
  • 11
  • 2
  • PDF
Jacobi–Jordan algebras
Abstract We study finite-dimensional commutative algebras, which satisfy the Jacobi identity. Such algebras are Jordan algebras. We describe some of their properties and give a classification inExpand
  • 10
  • 2
  • PDF
...
1
2
3
4
5
...