Smoothness Theorem for Differential BV Algebras
John Terilla
TL;DR
This paper establishes conditions under which the quantum differential graded Lie algebra associated with a differential BV algebra is smooth formal, linking it to the degeneration of a noncommutative Hodge to de Rham spectral sequence.
Contribution
It provides necessary and sufficient conditions for the quantum dgLa to be smooth formal, extending the classical case and connecting to spectral sequence degeneration.
Findings
Quantum dgLa is smooth formal under specific conditions.
Classical dgLa is always smooth formal.
Degeneration of a noncommutative Hodge to de Rham spectral sequence characterizes smoothness.
Abstract
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. References added.
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