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Tilted Algebras
Let $A$ be a finite dimensional hereditary algebra over a field, with $n$ simple $A$-modules. An $A$-module $T_A$ with $n$ pairwise nonisomorphic indecomposable direct summands and satisfying ${\text {Ex}}{{\text {t}}^1}({T_A}, {T_A}) = 0$ is called a tilting module, and its endomorphism ring $B$ is a tilted algebra. A tilting module …