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 representation varieties.
Graded Necklace Lie Bialgebras and Batalin-Vilkovisky Formalism
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
fields
math.QA 1years
2025 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
Quartic BV structures in supercategories and modified necklace Lie bialgebras
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 representation varieties.