%0 Journal Article
%T The higher relation bimodule
%A Ibrahim Assem
%A M. Andrea Gatica
%A Ralf Schiffler
%J Mathematics
%D 2011
%I arXiv
%X Given a finite dimensional algebra A of finite global dimension, we consider the trivial extension of A by the A-A-bimodule $\oplus_{i\ge 2} \Ext^2_A(DA,A)$, 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.
%U http://arxiv.org/abs/1111.6235v1