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arXiv · 2406.15266

Graded Necklace Lie Bialgebras and Batalin-Vilkovisky Formalism

Nikolai Perry·Ján Pulmann
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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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BibTeXRIS

Nikolai Perry, Ján Pulmann. 2024-06-21. Graded Necklace Lie Bialgebras and Batalin-Vilkovisky Formalism. https://arxiv.org/abs/2406.15266

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