Abstract
Given a finite dimensional algebra A of finite global dimension, we consider the trivial extension of A by the A − A-bimodule \(\oplus_{i\ge 2} {\rm Ext}^i_A(DA,A)\), 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.
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Dedicated to Idun Reiten for her 70th birthday.
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Assem, I., Gatica, M.A. & Schiffler, R. The Higher Relation Bimodule. Algebr Represent Theor 16, 979–999 (2013). https://doi.org/10.1007/s10468-012-9342-6
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DOI: https://doi.org/10.1007/s10468-012-9342-6