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arXiv · 2511.01410

Derived operations satisfy standard identities

Vladimir Dotsenko
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Abstract

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 $\mathbb{R}^n$, satisfies standard identities.

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Vladimir Dotsenko. 2025-11-03. Derived operations satisfy standard identities. https://doi.org/10.1007/s00574-025-00494-z

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