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Graded Necklace Lie Bialgebras and Batalin-Vilkovisky Formalism

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arxiv 2406.15266 v1 pith:PGTZZIRX submitted 2024-06-21 math.QA math-phmath.MP

Nikolai Perry , Ján Pulmann This is my paper · ORCID
classification math.QAmath-phmath.MP
keywords batalin-vilkoviskytracebialgebragradednecklacequiverstructurealgebra
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abstract

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.

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  1. Quartic BV structures in supercategories and modified necklace Lie bialgebras

    math.QA 2025-09 conditional novelty 7.0 of 10

    The augmented necklace Lie bialgebra, whose bracket and cobracket insert rather than remove involution pairs of arrows, is claimed to satisfy the IBL axioms and is witnessed by quartic Poisson/BV structures on represe...

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