Abstract
In this paper, for finite dimensional, basic, and connected algebras over a field, we give a sufficient condition, related to 2-cocycles, for Hochschild extension algebras to be symmetric. Moreover, we define the normalized 2-cocycle associated with a complete set of primitive orthogonal idempotents, and we show that for every 2-cocycle there exists a normalized 2-cocycle such that their cohomology classes coincide.
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Acknowledgements
The author thanks the referee for the valuable comments and helpful suggestions. This work was supported by the Japan Society for the Promotion of Science, Grant-in-Aid for Young Scientists (B) No. 17K14175.
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Itagaki, T. Symmetric Hochschild extension algebras and normalized 2-cocycles. Arch. Math. 112, 249–259 (2019). https://doi.org/10.1007/s00013-018-1249-y
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DOI: https://doi.org/10.1007/s00013-018-1249-y