Deformation-obstruction theory for diagrams of algebras and applications to geometry

DOI10.4171/JNCG/385zbMath1479.16028arXiv1806.05142MaRDI QIDQ2032775

Yaël Frégier, Severin Barmeier

Publication date: 14 June 2021

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.05142

zbMATH Keywords

deformations of associative algebras\(L_\infty\) algebrasGerstenhaber-Schack complex

Mathematics Subject Classification ID

Deformation quantization, star products (53D55) Deformations of associative rings (16S80) Deformations and infinitesimal methods in commutative ring theory (13D10) Formal methods and deformations in algebraic geometry (14D15)

Related Items

Operadic structure on the Gerstenhaber-Schack complex for prestacks, Quantizations of local surfaces and rebel instantons, Homotopy Rota-Baxter operators and post-Lie algebras, A survey on deformations, cohomologies and homotopies of relative Rota–Baxter Lie algebras, Lie \(n\)-algebras and cohomologies of relative Rota-Baxter operators on \(n\)-Lie algebras, Lie 3-algebras and deformations of relative Rota-Baxter operators on 3-Lie algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Simultaneous deformations of algebras and morphisms via derived brackets
• Non-commutative deformations and quasi-coherent modules
• Lectures on Duflo isomorphisms in Lie algebra and complex geometry
• From Poisson algebras to Gerstenhaber algebras
• Seiberg-Witten prepotential from instanton counting
• Derived brackets
• The Nekrasov conjecture for toric surfaces
• The \(L_\infty\)-deformation complex of diagrams of algebras
• Instantons on noncommutative \(\mathbb{R}^4\), and \((2,0)\) superconformal six dimensional theory
• Kontsevich star product on the dual of a Lie algebra
• The Gerstenhaber-Schack complex for prestacks
• Classical deformations of noncompact surfaces and their moduli of instantons
• Deformation quantization of Poisson manifolds
• The cohomology structure of an associative ring
• On global deformation quantization in the algebraic case
• Higher derived brackets and homotopy algebras
• Hochschild cohomology of Abelian categories and ringed spaces
• On the deformation of rings and algebras
• Deformations of Algebraic Schemes
• Deformation theory of abelian categories
• Simultaneous deformations and Poisson geometry
• Algebroid prestacks and deformations of ringed spaces
• Deformation quantization of algebraic varieties.