# Weighted surface algebras: general version

## TL;DR

This paper introduces a broad class of weighted surface algebras based on triangulated surfaces with various orientations, establishing their fundamental properties and classifying their periodicity and symmetry.

## Contribution

It generalizes weighted surface algebras to include arbitrarily oriented triangles and characterizes their symmetry, tameness, and periodicity properties.

## Key findings

- Most of these algebras are symmetric tame periodic algebras of period 4.
- Excluded cases include singular disc, triangle, tetrahedral, and spherical algebras.
- The paper provides foundational properties of these generalized algebras.

## Abstract

We introduce general weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles and describe their basic properties. In particular, we prove that all these algebras, except the singular disc, triangle, tetrahedral and spherical algebras, are symmetric tame periodic algebras of period 4.