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Higher preprojective algebras and higher zigzag algebras

Presented by: 
Joseph Grant University of East Anglia
Date: 
Tuesday 28th March 2017 -
16:00 to 17:00
Venue: 
INI Seminar Room 1
Abstract: 
Co-author: Osamu Iyama (Nagoya University)
 
I will give a brief introduction to preprojective algebras and higher preprojective algebras, using examples. Then I will explain some results about certain higher preprojective algebras that were obtained in joint work with Osamu Iyama, including results on periodicity and descriptions of these algebras as (higher) Jacobi algebras of quivers with potential. Finally I will explain how, in simple cases, one can define higher zigzag algebras, generalizing certain algebras studied by Huefrano and Khovanov which appear widely in geometry and representation theory. As in the classical case, one finds interesting relations between spherical twists on the derived categories of these algebras.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons