Gabriele Bocca (University of East Anglia, Norwich), Quasi-hereditary covers of higher zigzag algebras.

Abstract:

In this talk we will define and investigate some quasi-hereditary covers for higher zigzag algebras. After recalling the definition and basic properties of higher zigzag algebras from [Gra17], we will construct quasi-hereditary covers for these algebras and we will show how they satisfy three different Koszul properties: they are Koszul in the classical sense, standard Koszul and Koszul with respect to the standard module Δ, according with the definition given in [Mad11]. This last property gives rise to a well defined duality and the Δ-Koszul dual will be computed as the path algebra of a quiver with relations.

References

[Mad11] D. O. Madsen, On a common generalization of Koszul duality and tilting equivalence, Advances in Mathematics (2011), vol.227, no.6, 2327-2348

[Gra17] J. Grant, Higher zigzag-algebras, ArXiv e-prints, arXiv:1711.00794v2