A simple construction of associative deformations A. A. Sharapov, E. D. Skvortsov
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ArticleSubject(s): деформационное квантование | пуассоновы структуры | симплектические алгебры отраженияGenre/Form: статьи в журналах Online resources: Click here to access online
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Letters in mathematical physics Vol. 109, № 3. P. 623-641Abstract: 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.
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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.
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