Ja n 20 06 Cluster - tilted algebras as trivial extensions
نویسندگان
چکیده
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 2 C (DC, C) of C by the CC -bimodule Ext 2 C (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 algebrã 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.
منابع مشابه
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