On Frobenius and separable algebra extensions in monoidal categories: applications to wreaths

  • Daniel Bulacu

    University of Bucharest, Romania
  • Blas Torrecillas

    Universidad de Almería, Almeria, Spain

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