Deformations of Path Algebras of Quivers with Relations

Explore the second lecture of a four-part minicourse on deformations of path algebras of quivers with relations. Delve into the intricate world of representation theory and algebraic geometry as lecturers Severin Barmeier and Zhengfang Wang guide you through 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. Gain insights into related topics such as noncommutative Gröbner bases, L-infinity algebras in deformation theory, algebraization of formal deformations, and deformation quantization of Poisson structures. Designed to be accessible for non-experts, this 59-minute lecture from the Hausdorff Center for Mathematics includes numerous examples to reinforce your understanding of these complex concepts.