Derived Operations Satisfy Standard Identities
Dotsenko V.
March 2026Springer Science and Business Media Deutschland GmbH
Bulletin of the Brazilian Mathematical Society
2026#57Issue 1
A derived operation is a bilinear operation on a commutative associative algebra A defined intrinsically out of its product and several derivations of the product. We show that operators of left (or right) multiplications of a derived operation always satisfy a “standard identity” of certain order. In particular, it implies that each Rankin–Cohen bracket of modular forms, as well as each higher bracket of Kontsevich’s universal deformation quantization formula for Poisson structures on Rn, satisfies standard identities.
Bilinear operation , Derived operation , Kontsevich’s universal deformation quantization , Rankin–Cohen bracket , Standard identity
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Institut de Recherche Mathématique Avancée, Université de Strasbourg, 7 rue René-Descartes, Strasbourg, 67000, France
Institute of Mathematics and Mathematical Modeling, Pushkin St. 125, Almaty, 050010, Kazakhstan
Institut de Recherche Mathématique Avancée
Institute of Mathematics and Mathematical Modeling
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