Abstract
We study the problem of classification of simple transitive 2-representations for the (non-finitary) 2-category of bimodules over the dual numbers. We show that simple transitive 2-representations with finitary apex are necessarily of rank 1 or 2, and those of rank 2 are exactly the cell 2-representations. For 2-representations of rank 1, we show that they cannot be constructed using the approach of (co)algebra 1-morphisms. We also propose an alternative definition of (co-)Duflo 1-morphisms for finitary 2-categories and describe them in the case of bimodules over the dual numbers.
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Acknowledgments
The author wants to thank her supervisor Volodymyr Mazorchuk for many valuable discussions, and Pedro Vaz for helpful comments on the manuscript. Thanks also to the referee for their constructive input.
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Open access funding provided by Uppsala University. This research is partially supported by Göran Gustafssons Stiftelse.
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Jonsson, H. On Simple Transitive 2-representations of Bimodules over the Dual Numbers. Algebr Represent Theor 26, 2057–2083 (2023). https://doi.org/10.1007/s10468-022-10167-w
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DOI: https://doi.org/10.1007/s10468-022-10167-w