Orthogonality conjecture for the bimodule summands of a tilted algebra

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Let CC be a tilted algebra, and let E=Ext⁡C2(DC,C)E=\operatorname{Ext}_{C}^{2}(DC,C). Regard EE as a CC-CC-bimodule and decompose it into indecomposable summands. Orthogonality conjecture. The indecomposable summands of EE as a CC-CC-bimodule are pairwise orthogonal bricks. This claim describes the structure of the extension bimodule associated with a tilted algebra; the supplied text does not state whether it has been proved or refuted.

References

Primary source

Ibrahim Assem, Juan Carlos Bustamante, Kiyoshi Igusa and Ralf Schiffler, “The first Hochschild cohomology group of a cluster-tilted algebra revisited”, arXiv:1209.2146 (2013).

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