报告题目:Quasi differential calculi and cyclic opposite  operad modules with pairingwith applications to   hom-associative algebras

报告专家: 吕为国（中国科学技术大学）

报告时间: 2021年12月11日(周六)，10:30-11:20

报告地点：理工H楼H113

报告摘要：We show that a cyclic opposite operad module over a nonsymmetric operad with multiplicationgives rise to a quasi differential calculus structure at the chain level and thus a Tamarkin-Tsygan calculus at the homology level. We define cyclic opposite modules with pairing and show that in this case the cochain complex of the nonsymmetric operads with multiplication is a Quesney homotopy Batalin-Vilkovisky(BV for short) algebraand thus its cohomology  is a  BV algebra.We apply our results to hom-associative algebras. We prove that the Hochschild homology and cohomology complexes of a strictly unital Hom-associative algebra form a quasi differential calculus. As a consequence, we deduce that the Hochschild homology and cohomology form a differential calculus.    Furthermore, we also define a Hom-symmetric Frobenius algebra and prove that its Hochschild cochain complex is Quesney homotopy BV algebra, whose    cohomology becomes a BV algebra.（joint work with  Yu Ye and Guodong Zhou）

欢迎各位老师、同学届时前往！

数学科学学院

2021年12月8日

专家简介:吕为国，中国科学技术大学博士后。2019年6月毕业于华东师范大学数学科学学院，获得理学博士学位，主要研究Hochschild 上同调理论,已发表多篇SCI论文。