English

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 ΔeS/=0\Delta e^{S/\hbar} = 0 and the category of IBL{\rm 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 IBL{\rm IBL}_\infty-algebras and L{\rm 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.

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