The locally complexified-gentle algebras

TL;DR

This paper introduces a new class of real algebras called locally complexified-gentle algebras, showing their Morita equivalence to semilinear clannish algebras via modulated quivers.

Contribution

It defines locally complexified-gentle algebras and demonstrates their Morita equivalence to semilinear clannish algebras using modulated quivers.

Findings

Two types of locally complexified-gentle algebras are introduced.

They are Morita equivalent to semilinear clannish algebras.

The approach uses modulated quivers.

Abstract

We call an $\mathbb{R}$-algebra locally complexified-gentle if it becomes a locally gentle $\mathbb{C}$-algebra up to Morita equivalence after complexification. We use modulated quivers to introduce two types of locally complexified-gentle algebras and show that they are Morita equivalent to some semilinear clannish algebras.