A simple construction of associative deformations

Abstract

We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain first-order deformations of A extend to all orders and we derive explicit recurrent formulas determining this extension. In physical terms, this may be regarded as the deformation quantization of noncommutative Poisson structures on A.

17 pages, journal version

References in corpus (1)

• Hochschild cohomology of the Weyl algebra and Vasiliev's equations

Cited by in corpus (4)

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• Minimal model of Chiral Higher Spin Gravity
• $A_{\infty }$ Algebras from Slightly Broken Higher Spin Symmetries
• On deformations of $A_{\infty }$-algebras