Abstract
In this paper, we show the existence of the attached comultiplication structure on $\operatorname{Hom}_{eAe}(eA,D(Ae))$ if an $(eAe,A)$-bimodule $eA$ has the double centraliser property over an algebra $A$ with the idempotent $e$. Then we apply it on gendo-Gorenstein algebras. As applications, we give a sufficient and necessary condition for a gendo-Gorenstein algebra to be Gorenstein, and give a bocs-theoretic characterisation of the double centraliser property.
Funding Statement
The first author is supported by the National Natural Science Foundation of China (Grant Nos. 11771272 and 11871326).
Acknowledgments
The part of this paper was written during the first author's visit to Stuttgart in 2019. She would like to express their gratitude to Steffen Koenig for hospitality and many useful discussions.
Citation
Nan Gao. Jing Ma. Juxia Zhang. "Canonical Comultiplication and Double Centraliser Property." Taiwanese J. Math. 27 (1) 39 - 52, February, 2023. https://doi.org/10.11650/tjm/220903
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