# Algebras of generalized dihedral type

## TL;DR

This paper classifies all algebras of generalized dihedral type, extending known classes related to blocks with dihedral defect groups, using surface triangulations to describe their quivers and relations.

## Contribution

It provides a complete classification of generalized dihedral type algebras, linking them to surface triangulations and quiver relations, expanding understanding of their structure.

## Key findings

- Complete classification of generalized dihedral type algebras
- Description via surface triangulations and quivers
- Extension of known algebras related to dihedral defect groups

## Abstract

We provide a complete classification of all algebras of generalised dihedral type, which are natural generalizations of algebras which occurred in the study of blocks with dihedral defect groups. This gives a description by quivers and relations coming from surface triangulations.