The higher relation bimodule

Details The higher relation bimodule The higher relation bimodule

2011-11-27

arxiv.org/abs/1111.6235v1

Mathematics

Representation Theory

20 pages

Scientific paper

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.

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