域Z_3上三维李双代数的Atiyah class
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摘要
本文基于李代数上同调与李双代数的Atiyah class的相关理论计算了域Z_3上所有三维李双代数的Atiyah class.
Based on the theory of Lie algebra cohomology and the definition of the Atiyah class of a Lie bialgebra, Atiyah classes of all three-dimensional Lie bialgebras over Z_3 are calculated.
Based on the theory of Lie algebra cohomology and the definition of the Atiyah class of a Lie bialgebra, Atiyah classes of all three-dimensional Lie bialgebras over Z_3 are calculated.
引文
[1]Atiyah M F.Complex analytic connections in fibre bundles[J].Trans Amer Math Soc,1957,85:181.
[2]Molino P.Classe d′Atiyah d′un feuilletage et connexions transverses projetables[J].C R Acad Sci Paris Sér A-B,1971,272:A779.
[3]Wang H C.On invariant connections over a principal fibre bundle[J].Nagoya Math J,1958,13:1.
[4]Nguyen V H.Relations entre les diverses obstructions relationsàl′existence d′une connexion linéaire invariante sur un expace homogène[J].C RAcad Sci Paris,1965,260:45.
[5]Bordemann M.Atiyah classes and equivariant connections on homogeneous spaces[J].Trav Math,2012,20:29.
[6]Kapranov M M.Rozansky-Witten invariants via Atiyah classes[J].Compos Math,1999,115:71.
[7]Kontsevich M.Rozansky-Witten invariants via formal geometry[J].Compos Math,1999,115:115.
[8]Chen Z,Stiénon M,Xu P.From Atiyah classes to homotopy Leibniz algebras[J].Comm Math Phys,2016,341:309.
[9]Metha R A,Stiénon M,Xu P.The Atiyah class of a dg-vector bundle[J].C R Math Acad Sci Paris,2015,353:357.
[10]Voglaire Y,Xu P.Rozansky-Witten-type invariants from symplectic Lie pairs[J].Comm Math Phys,2015,336:217.
[11]Calaque D,Van den Bergh M.Hochschild cohomology and Atiyah classes[J].Adv Math,2010,224:1839.
[12]Hong W.Atiyah classes of Lie bialgbras[J].J Lie Theory,2019,29:263.
[13]Michaelis W.A class of infinite-dimensional Lie bialgebras containing the Virasoro algebra[J].Adv Math,1994,107:365.
[14]Taft E J.Witt and Virasoro algebras as Lie bialgebras[J].J Pure Appl Algebra,1993,87:301.
[15]Ng S H,Taft E J.Classification of the Lie bialgebras structures on the Witt and Virasoro algebras[J].J Pure Appl Algebra,2000,151:67.
[16]Kosmann-Schwarzbach Y.Lie bialgebras,Poisson Lie groups and dressing transformations[C]//Integrability of nonlinear systems(Pondicherry 1996),Berlin:Springer,1997:104.
[17]Hong W,Liu Z J.Lie bialgebras on k3 and Lagrange varieties[J].J Lie Theory,2009,19:639.
[18]李平,乔雨.复数域上三维李双代数的Atiyah class[J].吉林大学学报,2019,1:21.
[2]Molino P.Classe d′Atiyah d′un feuilletage et connexions transverses projetables[J].C R Acad Sci Paris Sér A-B,1971,272:A779.
[3]Wang H C.On invariant connections over a principal fibre bundle[J].Nagoya Math J,1958,13:1.
[4]Nguyen V H.Relations entre les diverses obstructions relationsàl′existence d′une connexion linéaire invariante sur un expace homogène[J].C RAcad Sci Paris,1965,260:45.
[5]Bordemann M.Atiyah classes and equivariant connections on homogeneous spaces[J].Trav Math,2012,20:29.
[6]Kapranov M M.Rozansky-Witten invariants via Atiyah classes[J].Compos Math,1999,115:71.
[7]Kontsevich M.Rozansky-Witten invariants via formal geometry[J].Compos Math,1999,115:115.
[8]Chen Z,Stiénon M,Xu P.From Atiyah classes to homotopy Leibniz algebras[J].Comm Math Phys,2016,341:309.
[9]Metha R A,Stiénon M,Xu P.The Atiyah class of a dg-vector bundle[J].C R Math Acad Sci Paris,2015,353:357.
[10]Voglaire Y,Xu P.Rozansky-Witten-type invariants from symplectic Lie pairs[J].Comm Math Phys,2015,336:217.
[11]Calaque D,Van den Bergh M.Hochschild cohomology and Atiyah classes[J].Adv Math,2010,224:1839.
[12]Hong W.Atiyah classes of Lie bialgbras[J].J Lie Theory,2019,29:263.
[13]Michaelis W.A class of infinite-dimensional Lie bialgebras containing the Virasoro algebra[J].Adv Math,1994,107:365.
[14]Taft E J.Witt and Virasoro algebras as Lie bialgebras[J].J Pure Appl Algebra,1993,87:301.
[15]Ng S H,Taft E J.Classification of the Lie bialgebras structures on the Witt and Virasoro algebras[J].J Pure Appl Algebra,2000,151:67.
[16]Kosmann-Schwarzbach Y.Lie bialgebras,Poisson Lie groups and dressing transformations[C]//Integrability of nonlinear systems(Pondicherry 1996),Berlin:Springer,1997:104.
[17]Hong W,Liu Z J.Lie bialgebras on k3 and Lagrange varieties[J].J Lie Theory,2009,19:639.
[18]李平,乔雨.复数域上三维李双代数的Atiyah class[J].吉林大学学报,2019,1:21.
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