Quartic BV structures in supercategories and modified necklace Lie bialgebras
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918138275168256 |
|---|---|
| author | Perry, Nikolai |
| author_facet | Perry, Nikolai |
| contents | We introduce a modified version of the necklace Lie bialgebra associated to a quiver, in which the bracket and cobracket insert (rather than remove) pairs of arrows in involution. This structure is then related to canonical quartic Poisson/Batalin-Vilkovisky structures on suitable representation varieties of the quiver. Constructions on the representation side take place in symmetric monoidal $Π$-categories, which prompts a discussion of graded differential operators on commutative monoids in any such category. The generality of the categorical approach allows us to fully recover necklace structures, showing how the modified and classical necklace operations are related via dualisability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07975 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quartic BV structures in supercategories and modified necklace Lie bialgebras Perry, Nikolai Quantum Algebra Representation Theory Symplectic Geometry We introduce a modified version of the necklace Lie bialgebra associated to a quiver, in which the bracket and cobracket insert (rather than remove) pairs of arrows in involution. This structure is then related to canonical quartic Poisson/Batalin-Vilkovisky structures on suitable representation varieties of the quiver. Constructions on the representation side take place in symmetric monoidal $Π$-categories, which prompts a discussion of graded differential operators on commutative monoids in any such category. The generality of the categorical approach allows us to fully recover necklace structures, showing how the modified and classical necklace operations are related via dualisability. |
| title | Quartic BV structures in supercategories and modified necklace Lie bialgebras |
| topic | Quantum Algebra Representation Theory Symplectic Geometry |
| url | https://arxiv.org/abs/2509.07975 |