复数域上三维李双代数的Atiyah Class
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摘要
基于复数域上三维李双代数的结构分类,利用李双代数Atiyah class为零的充要条件,计算所有复数域上三维李双代数的Atiyah class.
Based on the structure classification of three dimensional Lie bialgebras over■,we calculated the Atiyah classes of all three dimensional Lie bialgebras over ■by using a sufficient and necessary condition for the Atiyah class of a Lie bialgebra to be zero.
Based on the structure classification of three dimensional Lie bialgebras over■,we calculated the Atiyah classes of all three dimensional Lie bialgebras over ■by using a sufficient and necessary condition for the Atiyah class of a Lie bialgebra to be zero.
引文
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[2]KAPRANOV M.Rozansky-Witten Invariants via Atiyah Classes[J].Compos Math,1999,115(1):71-113.
[3]MARKARIAN N.The Atiyah Class,Hochschild Cohomology and the Riemann-Roch Theorem[J].J Lond Math Soc,2009,79(1):129-143.
[4]CALAQUE D,BERGH M,Van den.Hochschild Cohomology and Atiyah Classes[J].Adv Math,2010,224(5):1839-1889.
[5]MEHTA R A,STIENON M,XU Ping.The Atiyah Class of a Dg-Vector Bundle[J].Comptes Rend Math,2015,353(4):357-362.
[6]CHEN Zhuo,STIENON M,XU Ping.From Atiyah Classes to Homotopy Leibniz Algebras[J].Commun Math Phys,2016,341(1):309-349.
[7]BATAKIDIS P,VOGLAIRE Y.Atiyah Classes and Dg-Lie Algebroids for Matched Pairs[J].J Geom Phys,2018,123:156-172.
[8]KOSMANN-SCHWARZBACH Y.Lie Bialgebras,Poisson Lie Groups and Dressing Transformations[C]//Proceedings of the CIMPA School Pondicherry University.Berlin:Springer,1997:104-170.
[9]HONG Wei.The Atiyah Classes of Lie Bialgebras[J/OL].2018-02-06.http://arxiv.org/pdf/1802.01937.pdf.
[10]HONG Wei,LIU Zhangju.Lie Bialgebras on K3 and Lagrange Varieties[J].J Lie Theor,2009,19(4):639-659.
[2]KAPRANOV M.Rozansky-Witten Invariants via Atiyah Classes[J].Compos Math,1999,115(1):71-113.
[3]MARKARIAN N.The Atiyah Class,Hochschild Cohomology and the Riemann-Roch Theorem[J].J Lond Math Soc,2009,79(1):129-143.
[4]CALAQUE D,BERGH M,Van den.Hochschild Cohomology and Atiyah Classes[J].Adv Math,2010,224(5):1839-1889.
[5]MEHTA R A,STIENON M,XU Ping.The Atiyah Class of a Dg-Vector Bundle[J].Comptes Rend Math,2015,353(4):357-362.
[6]CHEN Zhuo,STIENON M,XU Ping.From Atiyah Classes to Homotopy Leibniz Algebras[J].Commun Math Phys,2016,341(1):309-349.
[7]BATAKIDIS P,VOGLAIRE Y.Atiyah Classes and Dg-Lie Algebroids for Matched Pairs[J].J Geom Phys,2018,123:156-172.
[8]KOSMANN-SCHWARZBACH Y.Lie Bialgebras,Poisson Lie Groups and Dressing Transformations[C]//Proceedings of the CIMPA School Pondicherry University.Berlin:Springer,1997:104-170.
[9]HONG Wei.The Atiyah Classes of Lie Bialgebras[J/OL].2018-02-06.http://arxiv.org/pdf/1802.01937.pdf.
[10]HONG Wei,LIU Zhangju.Lie Bialgebras on K3 and Lagrange Varieties[J].J Lie Theor,2009,19(4):639-659.