The Bridgeland's Ringel-Hall algebra associated to an algebra with global dimension at most two
classification
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algebraringel-hallalgebrasdimensionglobalassociatedassociativebridgeland
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For any finitely dimensional associative algebra with global dimension $\leq 2$, we show that there is an embedding from the twisted Ringel-Hall algebra to the Brigeland's Ringel-Hall algebra. In particular, this result is true for tilted algebras and canonical algebras.
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