# Smoothness theorem for differential BV algebras

@article{Terilla2008SmoothnessTF,
title={Smoothness theorem for differential BV algebras},
author={John Terilla},
journal={Journal of Topology},
year={2008},
volume={1}
}
• John Terilla
• Published 9 July 2007
• Mathematics
• Journal of Topology
Given a differential Batalin–Vilkovisky algebra (V, Q, Δ.) the associated odd differential graded Lie algebra (V, Q, + Δ, [,].) is always smooth formal. The quantum differential graded Lie algebra Lℏ:=(V[[ℏ]],Q+ℏΔ,[,]) is not always smooth formal, but when it is — for example, when a Q‐Δ version of the ∂‐∂ Lemma holds — there is a weak Frobenius manifold structure on the homology of L that is important in applications and relevant to quantum correlation functions. In this paper, we prove that L…
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