Graded Necklace Lie Bialgebras and Batalin-Vilkovisky Formalism
arXiv:2406.15266
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 . We relate the resulting Batalin-Vilkovisky structure to the Batalin-Vilkovisky structure coming from a degree symplectic form on a suitably defined representation variety of the quiver . The morphism intertwining these Batalin-Vilkovisky algebras will be given by a twisted trace, recovering the usual (super)trace and the odd trace.
Accepted version (Selecta Mathematica), 32 pages