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2007

Smoothness Theorem for Differential BV Algebras

Terilla, John

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Associated to a differential BV algebra are two differential graded Lie algebras: we call one classical and the other, which contains a formal h-bar parameter, quantum.

The classical dgLa is always smooth formal.
In this paper, we give necessary and sufficient conditions for the quantum dgLa to be smooth formal.
These conditions are equivalent to the degeneration of a version of the noncommutative Hodge to de Rham spectral sequence.

Smoothness Theorem for Differential BV Algebras · Around

Built on

Frobenius manifolds and formality of Lie polyvector fields
S. Barannikov and M. Kontsevich · 1998
Earlier work this paper cites.
Frobenius Manifolds, Quantum Cohomology, and Moduli Spaces
Y. Manin · 1999
Earlier work this paper cites.

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Then

Quantum backgrounds and QFT, math.QA/0605459, 2006
J. S. Park, J. Terilla, and T. Tradler · 2006
Later among the works it cites.
Non-commutative Hodge-to-de Rham degeneration via the method of Deligne-Illusie
D.Kaledin · 2008
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