On m-cluster tilted algebras and trivial extensions

TL;DR

This paper explores the relationship between iterated tilted algebras and m-cluster tilted algebras, showing how the latter can be viewed as trivial extensions of derived equivalent iterated tilted algebras.

Contribution

It establishes that m-cluster tilted algebras can be obtained as trivial extensions of certain iterated tilted algebras and provides a method to identify these algebras.

Findings

m-cluster tilted algebras are trivial extensions of iterated tilted algebras

a procedure to find the related iterated tilted algebra is provided

m-cluster tilted algebras are quotients of higher relation extensions

Abstract

In this work we study the connection between iterated tilted algebras and m-cluster tilted algebras. We show that an iterated tilted algebra induces an m-cluster tilted algebra. This m-cluster tilted algebra can be seen as a trivial extension of another iterated tilted algebra which is derived equivalent to the original one. We give a procedure to find this new iterated tilted algebra. These m-cluster tilted algebras are quotients of higher relation extensions.