Noncommutative Hamiltonian structures and quantizations on preprojective algebras
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908375677140992 |
|---|---|
| author | Zhao, Hu |
| author_facet | Zhao, Hu |
| contents | Given a noncommutative Hamiltonian space $A$, we prove that the conjecture ``{\it quantization commutes with reduction}'' holds for $A$. We further construct a semidirect product algebra $A \rtimes \mG^A$, and establish a correspondence between equivariant sheaves on the representation space and left $A\rtimes\mG^A$-modules. In the quiver setting, using the quantum and classical trace maps, we establish the explicit correspondence between quantizations of a preprojective algebra and those of a quiver variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17578 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Noncommutative Hamiltonian structures and quantizations on preprojective algebras Zhao, Hu Quantum Algebra Mathematical Physics Rings and Algebras Representation Theory Given a noncommutative Hamiltonian space $A$, we prove that the conjecture ``{\it quantization commutes with reduction}'' holds for $A$. We further construct a semidirect product algebra $A \rtimes \mG^A$, and establish a correspondence between equivariant sheaves on the representation space and left $A\rtimes\mG^A$-modules. In the quiver setting, using the quantum and classical trace maps, we establish the explicit correspondence between quantizations of a preprojective algebra and those of a quiver variety. |
| title | Noncommutative Hamiltonian structures and quantizations on preprojective algebras |
| topic | Quantum Algebra Mathematical Physics Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2312.17578 |