The MV formalism for ${\mathrm{IBL}}_{\infty }$- and ${\mathrm{BV}}_{\infty }$-algebras

Abstract

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.

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

References in corpus (2)

• Homological algebra related to surfaces with boundary
• The Frobenius properad is Koszul

Cited by in corpus (1)

• Cumulants, Koszul brackets and homological perturbation theory for commutative $B{V}_{\infty }$ and $IB{L}_{\infty }$ algebras