Showing papers on "Differential graded Lie algebra published in 2004"
TL;DR: In this paper, it was shown that the cup product of a compact Kahler manifold can be lifted to an L∞-morphism from the Kodaira-Spencer differential graded Lie algebra to the suspension of the singular cohomology of the manifold.
26 citations
TL;DR: In this article, it was shown that solving the Maurer-Cartan equations is, essentially, the same as performing the Hamiltonian reduction construction of a differential graded Lie algebra equipped with an even nondegenerate invariant bilinear form gives rise to modular stacks with symplectic structures.
Abstract: We show that solving the Maurer-Cartan equations is, essentially, the same thing as performing the Hamiltonian reduction construction. In particular, any differential graded Lie algebra equipped with an even nondegenerate invariant bilinear form gives rise to modular stacks with symplectic structures.
10 citations
TL;DR: In this article, a class of easily constructible examples of L n and L ∞ structures on graded vector spaces with three one-dimensional components is presented, and sufficient conditions under which a space with an L 3 structure is a differential graded Lie algebra.
Abstract: L ∞ structures have been a subject of recent interest in physics, where they occur in closed string theory and in gauge theory. This paper provides a class of easily constructible examples of L n and L ∞ structures on graded vector spaces with three one-dimensional components. In particular, it demonstrates a way to classify all possible L n and L ∞ structures on V = V m ⊕ V m+1 ⊕ V m+2 when each of the three components is one-dimensional. Included are necessary and sufficient conditions under which a space with an L 3 structure is a differential graded Lie algebra. It is also shown that some of these differential graded Lie algebras possess a nontrivial L n structure for higher n.
5 citations
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TL;DR: In this paper, a new cohomology for Lie algebroids is introduced, which provides a differential graded Lie algebra which controls deformations of the structure bracket of the algebroid.
Abstract: We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases such as Lie algebras, Poisson manifolds, foliations, Lie algebra actions on manifolds.
2 citations
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TL;DR: In this article, a universal and a semi-universal deformation of the cotangent complex of a differential graded Lie algebra is defined in such a way that the bases of deformations are $L_\infty$-algebras, as well.
Abstract: In this paper, deformations of $L_\infty$-algebras are defined in such a way that the bases of deformations are $L_\infty$-algebras, as well. A universal and a semiuniversal deformation is constructed for $L_\infty$-algebras, whose cotangent complex admits a splitting. The paper also contains an explicit construction of a minimal $L_\infty$-structure on the homology $H$ of a differential graded Lie algebra $L$ and of an $L_\infty$-quasi-isomorphism between $H$ and $L$.
1 citations