Lagrangian Relations and Quantum $L_\infty$ Algebras
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910088704294912 |
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| author | Jurčo, Branislav Pulmann, Ján Zika, Martin |
| author_facet | Jurčo, Branislav Pulmann, Ján Zika, Martin |
| contents | Quantum $L_\infty$ algebras are higher loop generalizations of cyclic $L_\infty$ algebras. Motivated by the problem of defining morphisms between such algebras, we construct a linear category of $(-1)$-shifted symplectic vector spaces and distributional half-densities, originally proposed by Ševera. Morphisms in this category can be given both by formal half-densities and Lagrangian relations; we prove that the composition of such morphisms recovers the construction of homotopy transfer of quantum $L_\infty$ algebras. Finally, using this category, we propose a new notion of a relation between quantum $L_\infty$ algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06110 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lagrangian Relations and Quantum $L_\infty$ Algebras Jurčo, Branislav Pulmann, Ján Zika, Martin Mathematical Physics Quantum Algebra Symplectic Geometry Quantum $L_\infty$ algebras are higher loop generalizations of cyclic $L_\infty$ algebras. Motivated by the problem of defining morphisms between such algebras, we construct a linear category of $(-1)$-shifted symplectic vector spaces and distributional half-densities, originally proposed by Ševera. Morphisms in this category can be given both by formal half-densities and Lagrangian relations; we prove that the composition of such morphisms recovers the construction of homotopy transfer of quantum $L_\infty$ algebras. Finally, using this category, we propose a new notion of a relation between quantum $L_\infty$ algebras. |
| title | Lagrangian Relations and Quantum $L_\infty$ Algebras |
| topic | Mathematical Physics Quantum Algebra Symplectic Geometry |
| url | https://arxiv.org/abs/2401.06110 |