arXiv · math/0210261
The explicit list of all almost factorizable Lie bialgebra structures on real absolutely simple Lie algebras is given.
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Nicolas Andruskiewitsch, Patricia Jancsa. 2003-06-25. On simple real Lie bialgebras. https://arxiv.org/abs/math/0210261
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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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