Abstract
Given a finite-dimensional algebra C (over an algebraically closed field) of global dimension at most two, we define its relation-extension algebra to be the trivial extension C Ext C 2 (DC,C) of C by the C-C-bimodule Ext C 2 (DC,C). We give a construction for the quiver of the relation-extension algebra in case the quiver of C has no oriented cycles. Our main result says that an algebra C is cluster-tilted if and only if there exists a tilted algebra C such that C is isomorphic to the relation-extension of C.
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