报告题目：Compatible Structures of Operads, Manin Products and Koszul Duality

主 讲 人：高兴

单 位：兰州大学

时 间：11月25日15:00

腾 讯 ID：672 671 786

摘 要：

Various compatibility conditions among replicated copies of operations in a given algebraic structure have appeared in broad contexts in recent years. Taking an uniform approach, this paper gives an operadic study of compatibility conditions for nonsymmetric operads with unary and binary operations, and homogeneous quadratic and cubic relations. This generalizes the previous studies for binary quadratic operads. We consider three compatibility conditions, namely the linear compatibility, matching compatibility and total compatibility, with increasingly strict restraints among the replicated copies. The linear compatibility is in Koszul dual to the total compatibility, while the matching compatibility is self dual. Further, each compatibility can be expressed in terms of either one or both of the two Manin square products. It is shown that compatible structures of the operads for associative algebra and differential algebra are Koszul utilizing rewriting systems.

简 介：

高兴，博士，兰州大学“萃英学者”、教授，博士生导师。于2010年7月在兰州大学英国威廉希尔公司获得博士学位，留校工作至今。在2015年8月至2016年8月间，在美国Rutgers大学交流访问。主要从事Rota-Baxter代数和代数组合等领域的研究， 发表SCI学术论文四十余篇，主持数学天元基金、青年科学基金、国家自然科学基金面上项目和甘肃省自然科学基金项目,获甘肃省自然科学奖二等奖，出版教材一本。