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Abstract

A new approach to the construction of formal deformations of associative
algebras is proposed. It exploits the machinery of injective resolutions 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 $A$.