Associative half-densities on symplectic groupoids and quantization
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914583024762880 |
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| author | Cabrera, Alejandro Valenotti, Gabriel Gonzalo Ledesma |
| author_facet | Cabrera, Alejandro Valenotti, Gabriel Gonzalo Ledesma |
| contents | In this paper, we study half-densities enhancing the multiplication map on a symplectic groupoid and which satisfy a suitable associativity condition. This is structurally motivated by the expected complete semiclassical-analytic approximation to a star product for the underlying Poisson manifold. We show the existence and classification of such associative half-densities, and further apply this theory to the understanding of semiclassical factors in Kontsevich's quantization formula. In the particular case of a linear Poisson structure, we recover the factors appearing in the Duflo isomorphism and its Kashiwara-Vergne extensions as a canonical associative enhancement. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_08201 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Associative half-densities on symplectic groupoids and quantization Cabrera, Alejandro Valenotti, Gabriel Gonzalo Ledesma Symplectic Geometry Mathematical Physics 81S10, 53D55, 53D17 In this paper, we study half-densities enhancing the multiplication map on a symplectic groupoid and which satisfy a suitable associativity condition. This is structurally motivated by the expected complete semiclassical-analytic approximation to a star product for the underlying Poisson manifold. We show the existence and classification of such associative half-densities, and further apply this theory to the understanding of semiclassical factors in Kontsevich's quantization formula. In the particular case of a linear Poisson structure, we recover the factors appearing in the Duflo isomorphism and its Kashiwara-Vergne extensions as a canonical associative enhancement. |
| title | Associative half-densities on symplectic groupoids and quantization |
| topic | Symplectic Geometry Mathematical Physics 81S10, 53D55, 53D17 |
| url | https://arxiv.org/abs/2604.08201 |