Tuesday, March 27, 15:15, 7.527

Judith Marquardt (Bonn), Shod Nakayama algebras and pattern avoiding permutations

Abstract:
Algebras of small homological dimension, also called shod algebras, have recently been understood to be a generalisation of tilted algebras via silting theory. In an attempt to understand this class of algebras better, we study the class of Nakayama algebras and give a combinatorial classification when these are shod. We can restrict to linear Nakayama algebras which are in bijection with Dyck paths. Krattenthaler showed that these are again in bijection with 132-avoiding permutations. Pattern avoidance is a classical combinatorial problem which has links to many other fields. We give a combinatorial classification of Nakayama algebras of small homological dimension using the Krattenthaler bijection. Namely, we show that this bijection restricts to a bijection between shod Nakayama algebras and 132-avoiding permutations which additionally avoid certain other patterns.