Formality of Kapranov's brackets in K\"ahler geometry via pre-Lie deformation theory
作者： Ruggero Bandiera
DOI:
关键词:
摘要: We recover some recent results by Dotsenko, Shadrin and Vallette on the Deligne groupoid of a pre-Lie algebra, showing that they follow naturally variant PBW Theorem. As an application, we show Kapranov's $L_\infty$ algebra structure Dolbeault complex K\"ahler manifold is homotopy abelian independent choice metric up to isomorphism, making trivializing isomorphism explicit.
arxiv.org
core.ac.uk
harvard.edu参考文章(44)
Shoshichi Kobayashi, Differential geometry of complex vector bundles ,(1987)
Kurusch Ebrahimi-Fard, Alexander Lundervold, Hans Munthe-Kaas, On the Lie enveloping algebra of a post-Lie algebra arXiv: Numerical Analysis. ,(2014)
Johan Louis Dupont, Curvature and Characteristic Classes ,(1978)
Damien Calaque, Andrei Căldăraru, Junwu Tu, PBWfor an inclusion of Lie algebras Journal of Algebra. ,vol. 378, pp. 64- 79 ,(2013) , 10.1016/J.JALGEBRA.2012.12.008
Marco Manetti, Lectures on deformations of complex manifolds Rendiconti di Matematica e delle sue applicazioni. ,vol. 24, pp. 1- 183 ,(2004)
Benjamin Hennion, Tangent Lie algebra of derived Artin stacks arXiv: Algebraic Geometry. ,(2013) , 10.1515/CRELLE-2015-0065
Amnon Yekutieli, Continuous and Twisted L_infinity Morphisms arXiv: Quantum Algebra. ,(2005)
Braxton Livingston Collier, Infinitesimal Symmetries of Dixmier-Douady Gerbes arXiv: Differential Geometry. ,(2011)
Camille Laurent-Gengoux, Mathieu Stiénon, Ping Xu, Exponential map and L∞ algebra associated to a Lie pair Comptes Rendus Mathematique. ,vol. 350, pp. 817- 821 ,(2012) , 10.1016/J.CRMA.2012.08.009
Martin Markl, Higher Braces Via Formal (Non)Commutative Geometry arXiv: Algebraic Topology. pp. 67- 81 ,(2015) , 10.1007/978-3-319-18212-4_4