Higher zig-zag algebras

Joseph Grant (University of East Anglia)

Wednesday 18th January, 2017 16:00-17:00 Maths 522

Abstract

The name zigzag algebras was introduced by Huerfano and Khovanov, but examples of these algebras have been studied for a long time.  As well as appearing in the modular representation theory of finite groups, the zigzag algebras of type A Dynkin graphs control braid group actions on derived categories via spherical twists.  I will introduce a new general class of algebras with spherical indecomposable projective modules which includes the classical zigzag algebras as a special case.  This will be illustrated by an explicit example.  Parts of this work are joint with Osamu Iyama.

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