Quantizations of transposed Poisson algebras by Novikov deformations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908273889771520 |
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| author | Chen, Siyuan Bai, Chengming |
| author_facet | Chen, Siyuan Bai, Chengming |
| contents | The notions of the Novikov deformation of a commutative associative algebra and the corresponding classical limit are introduced. We show such a classical limit belongs to a subclass of transposed Poisson algebras, and hence the Novikov deformation is defined to be the quantization of the corresponding transposed Poisson algebra. As a direct consequence, we revisit the relationship between transposed Poisson algebras and Novikov-Poisson algebras due to the fact that there is a natural Novikov deformation of the commutative associative algebra in a Novikov-Poisson algebra. Hence all transposed Poisson algebras of Novikov-Poisson type, including unital transposed Poisson algebras, can be quantized. Finally, we classify the quantizations of $2$-dimensional complex transposed Poisson algebras in which the Lie brackets are non-abelian up to equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16056 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantizations of transposed Poisson algebras by Novikov deformations Chen, Siyuan Bai, Chengming Mathematical Physics Quantum Algebra Rings and Algebras 13D10, 13N15, 17A30, 17B63, 53D55 The notions of the Novikov deformation of a commutative associative algebra and the corresponding classical limit are introduced. We show such a classical limit belongs to a subclass of transposed Poisson algebras, and hence the Novikov deformation is defined to be the quantization of the corresponding transposed Poisson algebra. As a direct consequence, we revisit the relationship between transposed Poisson algebras and Novikov-Poisson algebras due to the fact that there is a natural Novikov deformation of the commutative associative algebra in a Novikov-Poisson algebra. Hence all transposed Poisson algebras of Novikov-Poisson type, including unital transposed Poisson algebras, can be quantized. Finally, we classify the quantizations of $2$-dimensional complex transposed Poisson algebras in which the Lie brackets are non-abelian up to equivalence. |
| title | Quantizations of transposed Poisson algebras by Novikov deformations |
| topic | Mathematical Physics Quantum Algebra Rings and Algebras 13D10, 13N15, 17A30, 17B63, 53D55 |
| url | https://arxiv.org/abs/2410.16056 |