Hochschild cohomology of the Weyl algebra and Vasiliev's equations

Abstract

We propose a simple injective resolution for the Hochschild complex of the Weyl algebra. By making use of this resolution, we derive explicit expressions for nontrivial cocycles of the Weyl algebra with coefficients in twisted bimodules as well as for the smash products of the Weyl algebra and a finite group of linear symplectic transformations. A relationship with the higher-spin field theory is briefly discussed.

15 pages; journal version

References in corpus (2)

• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• On Two Theorems About Symplectic Reflection Algebras

Cited by in corpus (7)

• Formal Higher Spin Gravities
• Type-B Formal Higher Spin Gravity
• Characteristic Cohomology and Observables in Higher Spin Gravity
• A simple construction of associative deformations
• On deformations of $A_{\infty }$-algebras
• Towards Massless Sector of Tensionless Strings on $Ad{S}_5$
• Categorical non-properness in wrapped Floer theory