报告题目: Title: Hom-Lie-Rinehart algebras.

报 告 人：Satyendra Kumar Mishra

报告时间：3月22日 2：00-2：50

报告地点：数学楼 617

摘 要: The notion of Lie-Rinehart algebra plays a crucial role in many branches of mathematics. In the last decade, there is a growing interest in hom-structures, and these structures are introduced for various classical algebraic and geometric objects. We define the notion of "Hom-Lie-Rinehart algebras" as an algebraic analogue of hom-Lie algebroids and also derive a canonical adjunction between the categories of hom-Lie-Rinehart algebras and hom-Gerstenhaber algebras. Next, we discuss the applications of our work for hom-Lie algebroids. It is known that there is a bijection between Hom-Lie algebroid structures on a hom-bundle and hom-Gerstenhaber algebra structures on the space of multisections of the underlying vector bundle. We further explore this relationship between different geometric structures on a hom-bundles and hom-algebraic structures on the space of multisections of the hom-bundle. In a sequel, we discuss extensions of hom-Lie-Rinehart algebra and address the problem of the lifting of automorphisms and derivations to central extensions. Finally, we associate a differential graded Lie algebra for a hom-Lie-Rinehart algebra, which controls its one-parameter formal deformations.

报告人简介：Satyendra Kumar Mishra 印度理工学院教师