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Mathematics > Algebraic Geometry

arXiv:0708.3977 (math)
[Submitted on 29 Aug 2007 (v1), last revised 16 Oct 2007 (this version, v2)]

Title:The Lie algebra perturbation lemma

Authors:Johannes Huebschmann (Universite de Lille 1)
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Abstract: Let g be a differential graded Lie algebra and suppose given a contraction of chain complexes of g onto a general chain complex M. We show that the data determine an sh-Lie algebra structure on M, that is, a coalgebra perturbation of the coalgebra differential on the cofree coaugmented differential graded cocommutative coalgebra S' on the suspension of M, a Lie algebra twisting cochain from the perturbed coalgebra S" to the given Lie algebra g, and an extension of this Lie algebra twisting cochain to a contraction of chain complexes from the Cartan-Chevalley-Eilenberg coalgebra on g onto S" which is natural in the data. This extends a result established in a joint paper of the author with J. Stashef [Forum math. 14 (2002), 847-868, math.AG/9906036] where only the particular where M is the homology of g has been explored.
Comments: 20 pages; in view of a number of comments of J. Stasheff, the exposition has been improved
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)
MSC classes: 16E45, 16W30, 17B55, 17B56, 17B65, 17B70, 18G10, 55P62
Cite as: arXiv:0708.3977 [math.AG]
  (or arXiv:0708.3977v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.0708.3977
Journal reference: In: Festschrift in honor of M. Gerstenhaber's 80-th and Jim Stasheff's 70-th birthday, Progress in Math. vol. 287, pp. 159--179, Birkhäuser-Verlag, Basel-Boston-Berlin, 2010

Submission history

From: Johannes Huebschmann [view email]
[v1] Wed, 29 Aug 2007 15:17:11 UTC (18 KB)
[v2] Tue, 16 Oct 2007 18:36:28 UTC (18 KB)
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