The Normalized Cochain Complex of a Nonsymmetric Cyclic Operad with Multiplication is a Quesney Homotopy BV Algebra

Abstract

We show that the normalized cochain complex of a nonsymmetric cyclic operad with multiplication is a Quesney homotopy BV algebra; as a consequence, the cohomology groups form a Batalin–Vilkovisky algebra, which is a result due to L. Menichi. We provide ample examples.

Keywords

Nonsymmetric operad / Cyclic operad / Gerstenhaber-Voronov algebra / Batalin–Vilkovisky algebra / Quesney homotopy BV algebra

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Funding

Fundamental Research Funds for the Central Universities(WK0010000061)

NSFC(11671139)

STCSM(13dz2260400)