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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 LSAs… Expand

178 11- PDF

Classification of Orbit Closures of 4-Dimensional Complex Lie Algebras

- D. Burde, C. Steinhoff
- Mathematics
- 15 April 1999

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

- D. Burde
- Mathematics
- 1 February 1998

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 is… Expand

45 8- PDF

DEGENERATIONS OF 7-DIMENSIONAL NILPOTENT LIE ALGEBRAS

- D. Burde
- Mathematics
- 16 September 2004

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 nilpotent… Expand

48 7- PDF

Simple left-symmetric algebras with¶solvable Lie algebra

- D. Burde
- Mathematics
- 1 March 1998

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 Lie… Expand

63 6- PDF

Degenerations of nilpotent Lie algebras

- D. Burde
- Mathematics
- 1999

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 of… Expand

33 3

AFFINE STRUCTURES ON NILMANIFOLDS

- D. Burde
- Mathematics
- 1 October 1996

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 obtain… Expand

86 2- PDF

Left-Invariant Affine Structures on Reductive Lie Groups

- D. Burde
- Mathematics
- 1 May 1996

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 Lie… Expand

39 2- PDF

Left-invariant affine structures on nilpotent Lie groups

- D. Burde
- Mathematics
- 1999

11 2- PDF

Jacobi–Jordan algebras

- D. Burde, A. Fialowski
- Mathematics
- 22 April 2014

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 in… Expand

10 2- PDF

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