Related papers: Derived coisotropic structures II: stacks and quan…

We study the shifted Poisson structure on the cochain complex C*(g) of a graded Lie algebra arising from shifted Lie bialgebra structure on g. We apply this to construct a 1-shifted Poisson structures on an infinitesimal quotient of the…

Generalized complex geometry was classically formulated by the language of differential geometry. In this paper, we reformulated a generalized complex manifold as a holomorphic symplectic differentiable formal stack in a homotopical sense.…

Let X be a smooth algebraic variety over a field of characteristic 0. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf O_X. These are stack-like versions of usual deformations. We prove that…

In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over general derived stacks, and give several examples of those. We…

The purpose of this paper is to study covariant Poisson structures on the complex Grassmannian obtained as quotients by coisotropic subgroups of the standard Poisson--Lie SU(n). Properties of Poisson quotients allow to describe Poisson…

This is a sequel of our previous work, arXiv:2209.09686, on the development of derived contact geometry, in which we formally introduced shifted contact structures on derived stacks and proved some results for $k$-shifted contact derived…

Let X be a smooth algebraic variety over a field K containing the real numbers. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf of X. These are stack-like versions of usual deformations. We…

We introduce the notions of shifted bisymplectic and shifted double Poisson structures on differential graded associative algebras, and more generally on non-commutative derived moduli functors with well-behaved cotangent complexes. For…

We investigate the quantization problem of $(-1)$-shifted derived Poisson manifolds in terms of $\BV_\infty$-operators on the space of Berezinian half-densities. We prove that quantizing such a $(-1)$-shifted derived Poisson manifold is…

We explain how any Artin stack $\mathfrak{X}$ over $\mathbb{Q}$ extends to a functor on non-negatively graded commutative cochain algebras, which we think of as functions on Lie algebroids or stacky affine schemes. There is a notion of…

In this note, we revisit the quantization of Lie bialgebras described by the second author, placing it in the more general framework of the quantization of moduli spaces developed in our previous work. In particular, we show that embeddings…

We examine shifted symplectic and Poisson structures on spaces of framed maps. We prove some results about shifted Poisson structures analogous to those in existing ones about symplectic structures. Then, we consider the space Map(X,D,Y) of…

We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We develop their underlying Lie theory, showing how these…

In this paper, we formally define the concept of shifted contact structures on derived (Artin) stacks and study their local properties in the context of derived algebraic geometry. In this regard, for negatively shifted contact derived…

In this note we construct a canonical lifting of arbitrary Poisson structures on a manifold to its algbera of densities. Using this construction we proceed to classify all extensions of a fixed structure on the original manifold to its…

We study certain Poisson structures related to quantized enveloping algebras. In particular, we give a description of the Poisson structure of a certain manifold associated to the ring of differential operators.

We introduce a new type of noncommutative Poisson structure on associative algebras. It induces Poisson structures on the moduli spaces classifying semisimple modules. Path algebras of doubled quivers and preprojective algebras have…

We extend the author's and CPTVV's correspondence between shifted symplectic and Poisson structures to establish a correspondence between exact shifted symplectic structures and non-degenerate shifted Poisson structures with formal…

It is proved that derived Quot-schemes, as defined by Ciocan-Fontanine and Kapranov, are represented by dg manifolds of finite type. This is the second part if a work aimed to analyze shifted symplectic structures on moduli spaces of…

We formulate a notion of $E_0$ quantisation of $(-1)$-Poisson structures on derived Artin $N$-stacks, and construct a map from $E_0$ quantisations of $(-1)$-shifted symplectic structures to power series in de Rham cohomology. For a square…