The MV formalism for ${\rm IBL}_\infty$- and ${\rm BV}_\infty$-algebras
Quantum Algebra
2017-02-28 v3 Algebraic Topology
Abstract
We develop a new formalism for the Quantum Master Equation and the category of -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 -algebras and -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.
Keywords
Cite
@article{arxiv.1511.01591,
title = {The MV formalism for ${\rm IBL}_\infty$- and ${\rm BV}_\infty$-algebras},
author = {Martin Markl and Alexander A. Voronov},
journal= {arXiv preprint arXiv:1511.01591},
year = {2017}
}
Comments
26 pages; this is a version accepted for publication in Lett. Math. Phys.; a new section on algebras of types other than commutative is added, a few minor changes made