On deformations of $A_{\infty }$-algebras

Abstract

A simple method is proposed for deforming $A_{\infty }$-algebras by means of the resolution technique. The method is then applied to the associative algebras of polynomial functions on quantum superspaces. Specifically, by introducing suitable resolutions, we construct explicit deformations of these algebras in the category of minimal $A_{\infty }$-algebras. The relation of these deformations to higher spin gravities is briefly discussed.

23 pages

References in corpus (7)

• $L_{\infty }$ Algebras and Field Theory
• Formal Higher Spin Gravities
• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• Homologie et cohomologie de Hochschild de certaines algebres polynomiales classiques et quantiques
• Homotopy Algebras of Differential (Super)forms in Three and Four Dimensions
• Hochschild cohomology of the Weyl algebra and Vasiliev's equations
• A simple construction of associative deformations

Cited by in corpus (5)

• Minimal model of Chiral Higher Spin Gravity
• Higher Spin Gravities and Presymplectic AKSZ Models
• On (spinor)-helicity and bosonization in $Ad{S}_4/CF{T}_3$
• Deformation quantization of the simplest Poisson Orbifold
• Chiral Higher Spin Gravity in (A)dS${}_4$ and secrets of Chern-Simons Matter Theories