The higher relation bimodule

IBRAHIM ASSEM, MARÍA ANDREA GATICA Y RALF SCHIFFLER

Algebras and Representation Theory

SPRINGER

Lugar: Berlin; Año: 2012 vol. 1 p. 1 - 21

1386-923X

Given a finite dimensional algebra $A$ of finite global dimension, we consider the trivial extension of $A$ by the $A-A$-bimodule $oplus_{ige 2} Ext^i_A(DA,A)$, which we call the higher relation bimodule. We first give a recipe allowing to construct the quiver of this trivial extension in case $A$ is a string algebra and then apply it to prove that, if $A$ is gentle, then the tensor algebra of the higher relation bimodule is gentle.