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.

Derived coisotropic structures I: affine case / Melani V.; Safronov P.. - In: SELECTA MATHEMATICA. - ISSN 1022-1824. - STAMPA. - 24:(2018), pp. 3061-3118. [10.1007/s00029-018-0406-2]

Derived coisotropic structures I: affine case

Melani V.;
2018

Abstract

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.
24
3061
3118
Melani V.; Safronov P.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/1285585
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