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

Authors：Lyu, Weiguo^*; Zhou, Guodong

Source：Communications in Mathematics and Statistics, 2022, 10(2): 299-330.

DOI：10.1007/s40304-020-00234-3

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

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.