Graded Necklace Lie Bialgebras and Batalin-Vilkovisky Formalism
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909228990464000 |
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| author | Perry, Nikolai Pulmann, Ján |
| author_facet | Perry, Nikolai Pulmann, Ján |
| contents | An involutive Lie bialgebra induces a Batalin-Vilkovisky operator on its exterior algebra. We introduce a graded generalization of the necklace Lie bialgebra, which depends on a choice of a quiver $Q$. We relate the resulting Batalin-Vilkovisky structure to the Batalin-Vilkovisky structure coming from a degree $-1$ symplectic form on a suitably defined representation variety of the quiver $Q$. The morphism intertwining these Batalin-Vilkovisky algebras will be given by a twisted trace, recovering the usual (super)trace and the odd trace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15266 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graded Necklace Lie Bialgebras and Batalin-Vilkovisky Formalism Perry, Nikolai Pulmann, Ján Quantum Algebra Mathematical Physics An involutive Lie bialgebra induces a Batalin-Vilkovisky operator on its exterior algebra. We introduce a graded generalization of the necklace Lie bialgebra, which depends on a choice of a quiver $Q$. We relate the resulting Batalin-Vilkovisky structure to the Batalin-Vilkovisky structure coming from a degree $-1$ symplectic form on a suitably defined representation variety of the quiver $Q$. The morphism intertwining these Batalin-Vilkovisky algebras will be given by a twisted trace, recovering the usual (super)trace and the odd trace. |
| title | Graded Necklace Lie Bialgebras and Batalin-Vilkovisky Formalism |
| topic | Quantum Algebra Mathematical Physics |
| url | https://arxiv.org/abs/2406.15266 |