Dietrich Burde

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Let g be a Lie algebra of dimension n over a field K . Then g determines a multiplication table relative to each basis {e1, . . . , en}. If [ei, ej] = ∑n k=1 γ k i,jek , then (γ k i,j) ∈ K n is called a structure for g and the γ i,j the structure constants of g. The elements of Ln(K) are exactly the Lie algebra structures. They form an affine algebraic(More)
In this paper we study degenerations of nilpotent Lie algebras. If λ, μ are two points in the variety of nilpotent Lie algebras, then λ is said to degenerate to μ , λ→deg μ , if μ lies in the Zariski closure of the orbit of λ . It is known that all degenerations of nilpotent Lie algebras of dimension n < 7 can be realized via a one-parameter subgroup. We(More)
We classify the cohomology spaces H(g,K) for all filiform nilpotent Lie algebras of dimension n ≤ 11 over K and for certain classes of algebras of dimension n ≥ 12. The result is applied to the determination of affine cohomology classes [ω] ∈ H(g,K). We prove the general result that the existence of an affine cohomology class implies an affine structure of(More)
We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov algebra is necessarily solvable. Conversely we present a 2-step solvable Lie algebra without any Novikov structure. We use extensions and classical r-matrices to construct Novikov structures on certain classes of(More)
We describe three methods to determine a faithful representation of small dimension for a finite-dimensional nilpotent Lie algebra over an arbitrary field. We apply our methods in finding bounds for the smallest dimension μ(g) of a faithful g-module for some nilpotent Lie algebras g. In particular, we describe an infinite family of filiform nilpotent Lie(More)