The MV formalism for \rm IBL_∞- and \rm BV_∞-algebras

2015/11/05 by Markl, Martin, Voronov, Alexander A.
#08C05 #16E45 #18G55 (Primary) #58A50 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1511.01591

Abstract

We develop a new formalism for the Quantum Master Equation Δe^S/ℏ = 0 and the category of \rm IBL_∞-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 \rm IBL_∞-algebras and \rm L_∞-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.

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