The MV formalism for IBL ∞ - and BV ∞ -algebras

Martin Markl; Alexander A. Voronov

doi:10.1007/s11005-017-0954-y

The MV formalism for IBL _∞ - and BV _∞ -algebras

Martin Markl, Alexander A. Voronov

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We develop a new formalism for the quantum master equation Δ e^S ^/ ^ħ= 0 and the category of IBL _∞-algebras and simplify some homotopical algebra arising in the context of oriented surfaces with boundary. We introduce and study a category of MV-algebras, which, on the one hand, contains such important categories as those of IBL _∞-algebras and L_∞-algebras and, on the other hand, is homotopically trivial, in particular allowing for a simple solution of the quantum master equation. We also present geometric interpretation of our results.

Original language	English (US)
Pages (from-to)	1515-1543
Number of pages	29
Journal	Letters in Mathematical Physics
Volume	107
Issue number	8
DOIs	https://doi.org/10.1007/s11005-017-0954-y
State	Published - Aug 1 2017

Bibliographical note

Funding Information:
The first author was supported by the Eduard Čech Institute P201/12/G028 and RVO: 67985840. The second author was supported by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan, and a Collaboration Grant from the Simons Foundation (#282349).

Funding Information:
The authors are indebted to D. Bashkirov and the anonymous referees for useful remarks, and to J. Latschev for sharing a preliminary version of his paper with K. Cieliebak and K. Fukaya. The first author also wishes to express his thanks to M. Doubek, B. Jurčo and I. Sachs for introducing him to the jungle of -algebras and acknowledge the hospitality of the University of Minnesota where he held the position of a Distinguished Ordway Visitor during the last stages of the work on this article. The second author gratefully acknowledges support from the Graduate School of Mathematical Sciences, the University of Tokyo, and the Simons Center for Geometry and Physics, Stony Brook University, at which some of the research for this paper was performed.

Publisher Copyright:
© 2017, Springer Science+Business Media Dordrecht.

Keywords

IBL -algebra
MV -algebra
Master equation
Transfer

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Cite this

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abstract = "We develop a new formalism for the quantum master equation Δ eS / ħ= 0 and the category of IBL ∞-algebras and simplify some homotopical algebra arising in the context of oriented surfaces with boundary. We introduce and study a category of MV-algebras, which, on the one hand, contains such important categories as those of IBL ∞-algebras and L∞-algebras and, on the other hand, is homotopically trivial, in particular allowing for a simple solution of the quantum master equation. We also present geometric interpretation of our results.",

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