Quantum Segre maps via cocycle twists
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913651920732160 |
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| author | Bazlov, Yuri Chen, Runyang |
| author_facet | Bazlov, Yuri Chen, Runyang |
| contents | A well-known noncommutative deformation $\mathcal A^N_{\mathbf{q}}$ of the polynomial algebra $\mathcal A^N$ can be obtained as a twist of $\mathcal A^N$ by a cocycle on the grading semigroup. Of particular interest to us is an interpretation of $A^N_{\mathbf{q}}$ as a quantum projective space. We outline a general method of cocycle twist quantization of tensor products and morphisms between algebras graded by monoids and use it to construct deformations of the classical Segre embeddings of projective spaces. The noncommutative Segre maps $s_{n,m}$, proposed by Arici, Galuppi and Gateva-Ivanova, arise as a particular case of our construction which corresponds to factorizable cocycles in the sense of Yamazaki. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08942 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Segre maps via cocycle twists Bazlov, Yuri Chen, Runyang Quantum Algebra 16S38, 20J06 A well-known noncommutative deformation $\mathcal A^N_{\mathbf{q}}$ of the polynomial algebra $\mathcal A^N$ can be obtained as a twist of $\mathcal A^N$ by a cocycle on the grading semigroup. Of particular interest to us is an interpretation of $A^N_{\mathbf{q}}$ as a quantum projective space. We outline a general method of cocycle twist quantization of tensor products and morphisms between algebras graded by monoids and use it to construct deformations of the classical Segre embeddings of projective spaces. The noncommutative Segre maps $s_{n,m}$, proposed by Arici, Galuppi and Gateva-Ivanova, arise as a particular case of our construction which corresponds to factorizable cocycles in the sense of Yamazaki. |
| title | Quantum Segre maps via cocycle twists |
| topic | Quantum Algebra 16S38, 20J06 |
| url | https://arxiv.org/abs/2501.08942 |