Nonsymmetric operads and various structures over cohomology theories
代数表示论团队学术报告
报告题目(Title)：Nonsymmetric operads and various structures over cohomology theories
报告人(Speaker)：吕为国 博士 (中国科学技术大学)
地点(Place)：教8楼209教室
时间(Time)：2019年10月31日 14:25-16:25
邀请人(Inviter)：刘玉明
报告摘要
We investigate how nonsymmetric operads with additional structures give rise to various structures over the corresponding cohomology groups and complexes. We show that the normalised cohomological complex of a nonsymmetric cyclic operad with multiplication is a homotopy BV algebra `a la Quesney; as a consequence, the cohomology groups form a Batalin-Vilkovisky algebra, which is a result due to L. Menichi in 2004. We define cyclic opposite operad modules with pairing and show that the existence of such cyclic opposite operad module with pairing implies that the operad is a cyclic operad and hence its cohomological complex is a Quesney algebra, continuing a line of research beginning by N. Kowalzig et al. We apply our results to hom-associative algebras. We prove that the Hochschild homology and cohomology of a strict unital Hom-associative algebra form a Tamarkin-Tsygan calculus. Furthermore, we also define a Hom-symmetric Frobenius algebra and prove that its Hochschild cochain complex is homotopy Batalin-Vilkovisky algebra `a la Quesney, whose Hochschild cohomology becomes a Batalin-Vilkovisky algebra.
