# Introduction to algebras of partial triangulations

## TL;DR

This paper introduces algebras derived from partial triangulations of marked surfaces, exploring their properties, relations to classical Jacobian and Brauer graph algebras, and their derived equivalences.

## Contribution

It provides a gentle introduction to these algebras, highlighting their structure, properties, and connections to existing algebra classes, with results proven in prior work.

## Key findings

- Algebras of partial triangulations have finite rank.
- They include Jacobian and Brauer graph algebras as special cases.
- Representation theory and derived equivalences are analyzed.

## Abstract

The aim of this note is to give a gentle introduction to algebras of partial triangulations of marked surfaces, following the structure of a talk given during the 49th symposium on ring theory and representation theory, held in Osaka. This class of algebras, which always have finite rank, contains classical Jacobian algebras of triangulations of marked surfaces and Brauer graph algebras. We discuss representation theoretical properties and derived equivalences. All results are proven in arXiv:1602.01592, under slightly milder hypotheses.