Deformations of Path Algebras of Quivers With Relations

Explore the final lecture of a four-part minicourse on deformations of path algebras of quivers with relations. Delve into advanced concepts in representation theory and algebraic geometry as presented by lecturers Severin Barmeier and Zhengfang Wang. Gain insights into the explicit description of deformation theory for finite quivers and finitely generated ideals of relations. Learn about reduction systems and their role in describing algebra deformations through systematic relation modifications. Examine related topics such as noncommutative Gröbner bases, L-infinity algebras in deformation theory, algebraization of formal deformations, and deformation quantization of Poisson structures. Benefit from an accessible approach designed for non-experts, complete with numerous examples to reinforce understanding of these complex mathematical concepts.