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

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 IBL infinity-algebras and L-infinity-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

• MV-algebra
• IBL infinity-algebra
• Master equation
• Transfer