Derived coisotropic structures I: affine case

• Valerio Melani ^[2] ; Pavel Safronov ^[1]
  1. [1] Université de Genève

     Université de Genève

     Genève, Suiza

     
  2. [2] Università di Milano, Italia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 4, 2018, págs. 3061-3118
• Idioma: inglés
• DOI: 10.1007/s00029-018-0406-2
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We define and study coisotropic structures on morphisms of commutative dg algebras in the context of shifted Poisson geometry, i.e. Pn-algebras. Roughly speaking, a coisotropic morphism is given by a Pn+1-algebra acting on a Pn-algebra. One of our main results is an identification of the space of such coisotropic structures with the space of Maurer–Cartan elements in a certain dg Lie algebra of relative polyvector fields. To achieve this goal, we construct a cofibrant replacement of the operad controlling coisotropic morphisms by analogy with the Swiss-cheese operad which can be of independent interest. Finally, we show that morphisms of shifted Poisson algebras are identified with coisotropic structures on their graph.