Atiyah classes and dg-Lie algebroids for matched pairs
作者： Panagiotis Batakidis , Yannick Voglaire
DOI: 10.1016/J.GEOMPHYS.2017.08.012
关键词: Class (set theory) 、 Algebra 、 Manifold 、 Mathematics 、 Vertical tangent 、 Morphism 、 Projection (linear algebra) 、 Matched pair 、 Pure mathematics 、 Structure (category theory)
摘要: Abstract For every Lie pair ( L , A ) of algebroids we construct a dg-manifold structure on the Z -graded manifold M = [ 1 ] ⊕ ∕ such that inclusion ι : → and projection p are morphisms dg-manifolds. The vertical tangent bundle T then inherits dg-Lie algebroid over . When comes from matched algebroids, show induces quasi-isomorphism sends Atiyah class this to pair. We also how (Atiyah classes of) pairs give rise dDG-algebras.
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sci-hub.se 参考文章(30)
Pavol Severa, Some title containing the words "homotopy" and "symplectic", e.g. this one arXiv: Symplectic Geometry. ,(2001)
Boris Shoikhet, On the Duflo formula for $L_\infty$-algebras and Q-manifolds arXiv: Quantum Algebra. ,(1998)
Damien Calaque, Carlo Rossi, Lectures on Duflo isomorphisms in Lie algebra and complex geometry European Mathematical Society Publishing House. ,(2011) , 10.4171/096
Alberto S. Cattaneo, Giovanni Felder, Relative formality theorem and quantisation of coisotropic submanifolds Advances in Mathematics. ,vol. 208, pp. 521- 548 ,(2007) , 10.1016/J.AIM.2006.03.010
Kevin J. Costello, A geometric construction of the Witten genus, I arXiv: Quantum Algebra. ,(2010)
Damien Calaque, Michel Van den Bergh, Hochschild cohomology and Atiyah classes Advances in Mathematics. ,vol. 224, pp. 1839- 1889 ,(2010) , 10.1016/J.AIM.2010.01.012
Rajan Amit Mehta, Q-algebroids and their cohomology Journal of Symplectic Geometry. ,vol. 7, pp. 263- 293 ,(2009) , 10.4310/JSG.2009.V7.N3.A1
I CIOCANFONTANINE, M KAPRANOV, Derived quot schemes Annales Scientifiques De L Ecole Normale Superieure. ,vol. 34, pp. 403- 440 ,(2001) , 10.1016/S0012-9593(01)01064-3
M. F. Atiyah, Complex analytic connections in fibre bundles Transactions of the American Mathematical Society. ,vol. 85, pp. 181- 207 ,(1957) , 10.1090/S0002-9947-1957-0086359-5
Maxim Kontsevich, Deformation Quantization of Poisson Manifolds Letters in Mathematical Physics. ,vol. 66, pp. 157- 216 ,(2003) , 10.1023/B:MATH.0000027508.00421.BF