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<p>A derived operation is a bilinear operation on a commutative associative algebra <i>A</i> 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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>, satisfies standard identities.</p>

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Derived Operations Satisfy Standard Identities

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Vladimir Dotsenko

摘要

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