On Frobenius and separable algebra extensions in monoidal categories: applications to wreaths
Daniel Bulacu
University of Bucharest, RomaniaBlas Torrecillas
Universidad de Almería, Almeria, Spain
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Abstract
We characterize Frobenius and separable monoidal algebra extensions in terms given by and . For instance, under some conditions, we show that the extension is Frobenius, respectively separable, if and only if is a Frobenius, respectively separable, algebra in the category of bimodules over . In the case when is separable we show that the extension is separable if and only if is a separable algebra. Similarly, in the case when is Frobenius and separable in a sovereign monoidal category we show that the extension is Frobenius if and only if is a Frobenius algebra and the restriction at of its Nakayama automorphism is equal to the Nakayama automorphism of . As applications, we obtain several characterizations for an algebra extension associated to a wreath to be Frobenius, respectively separable.
Cite this article
Daniel Bulacu, Blas Torrecillas, On Frobenius and separable algebra extensions in monoidal categories: applications to wreaths. J. Noncommut. Geom. 9 (2015), no. 3, pp. 707–774
DOI 10.4171/JNCG/206