Derived operations satisfy standard identities
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917097952509952 |
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| author | Dotsenko, Vladimir |
| author_facet | Dotsenko, Vladimir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derived operations satisfy standard identities Dotsenko, Vladimir Rings and Algebras 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. |
| title | Derived operations satisfy standard identities |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2511.01410 |