• Corpus ID: 189928397

Pre-Calabi-Yau algebras and double Poisson brackets

  title={Pre-Calabi-Yau algebras and double Poisson brackets},
  author={Natalia Iyudu and Maxim Kontsevich and Yannis Vlassopoulos},
  journal={arXiv: Rings and Algebras},
We give an explicit formula showing how the double Poisson algebra introduced in \cite{VdB} appears as a particular part of a pre-Calabi-Yau structure, i.e. cyclically invariant, with respect to the natural inner form, solution of the Maurer-Cartan equation on $A\oplus A^*$. Specific part of this solution is described, which is in one-to-one correspondence with the double Poisson algebra structures. The result holds for any associative algebra $A$ and emphasizes the special role of the fourth… 

Pre-Calabi-Yau algebras and noncommutative calculus on higher cyclic Hochschild cohomology

We prove $L_{\infty}$-formality for the higher cyclic Hochschild complex $\chH$ over free associative algebra or path algebra of a quiver. The $\chH$ complex is introduced as an appropriate tool for

A detailed look on actions on Hochschild complexes especially the degree 1 coproduct and actions on loop spaces

  • R. Kaufmann
  • Mathematics
    Journal of Noncommutative Geometry
  • 2022
We explain our previous results about Hochschild actions [Ka07,Ka08a] pertaining in particular to the co-product which appeared in a different form in [GH09] and provide a fresh look at the results.

Double Quasi-Poisson Algebras are Pre-Calabi-Yau

In this article, we prove that double quasi-Poisson algebras, which are noncommutative analogues of quasi-Poisson manifolds, naturally give rise to pre-Calabi-Yau algebras. This extends one of the



Noncommutative smooth spaces

We will work in the category Al gk of associative unital algebras over a fixed base field k. If A € Ob(Algk), we denote by 1A € A the unit in A and by m A : A ⊗ A—→A the product. For an algebra A, we

Notes on A∞-Algebras, A∞-Categories and Non-Commutative Geometry

We develop a geometric approach to A-infinity algebras and A-infinity categories based on the notion of formal scheme in the category of graded vector spaces. The geometric approach clarifies several

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We discuss double Poisson structures in sense of M. Van den Bergh on free associative algebras focusing on the case of quadratic Poisson brackets. We establish their relations with an associative

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In this paper we develop Poisson geometry for non-commutative algebras. This generalizes the bi-symplectic geometry which was recently, and independently, introduced by Crawley-Boevey, Etingof and

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We introduce relative noncommutative Calabi–Yau structures defined on functors of differential graded categories. Examples arise in various contexts such as topology, algebraic geometry, and

Deformation Quantization of Poisson Manifolds

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the


Some time ago B. Feigin, V. Retakh and I had tried to understand a remark of J. Stasheff [S1] on open string theory and higher associative algebras [S2]. Then I found a strange construction of

On the Deformation of Rings and Algebras

CHAPTER I. The deformation theory for algebras 1. Infinitesimal deformations of an algebra 2. Obstructions 3. Trivial deformations 4. Obstructions to derivations and the squaring operation 5.

Homotopy associativity of $H$-spaces. II