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八秩同辉校庆系列59 Operad of associative algebras with generalized derivation and Its application

来源: 发布时间: 2024-06-18 点击量:
  • 讲座人: 鲍炎红 教授
  • 讲座日期: 2024-6-21(周五)
  • 讲座时间: 10:30
  • 地点: 文津楼3211

讲座人简介:

鲍炎红,男,理学博士,安徽大学数学科学澳门新甫京教授、博士生导师,教务处副处长,入选2020年度教育部级青年学者,首批国家级一流本科课程《高等代数》负责人。

主要从事环与代数表示理论的研究,主持国家自然科学基金4项和安徽省杰出青年基金项目1项,在Adv. Math., Trans. Amer. Math. Soc., J. Algebra,Sci. China Math.等期刊上发表学术论文二十余篇,以第一完成人获安徽省自然科学二等奖1项。

讲座简介:

In this talk, we introduce the operad that encodes associative algebras equipped with a generalized derivation, and prove it is a Koszul operad. Using its Koszul dual operad, we construct the cohomology theory for an associative algegebra equipped with a generalized derivation. As an application, we study one-parameter formal deformations of an associative algebra with a generalized derivation and show they are controlled by the cohomology. Finally, we compute the Koszul dual cooperad and define the homotopy associative algebras with generalized derivations. This is a joint work with Jiangnan Xu.

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