The MV formalism for \({\mathrm{IBL}}_\infty \)- and \({\mathrm{BV}}_\infty \)-algebras. (English) Zbl 1382.16007
Summary: We develop a new formalism for the quantum master equation \(\Delta e^{S/\hslash } = 0\) and the category of \(\mathrm{IBL}_\infty \)-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 \(\mathrm{IBL}_\infty \)-algebras and \(\mathrm{L}_\infty \)-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.
MSC:
| 16E45 | Differential graded algebras and applications (associative algebraic aspects) |
| 18G55 | Nonabelian homotopical algebra (MSC2010) |
| 58A50 | Supermanifolds and graded manifolds |
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