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On Frobenius and separable algebra extensions in monoidal categories: applications to wreaths
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We characterize Frobenius and separable monoidal algebra extensions
i: R \to S
in terms given by
R
and
S
. For instance, under some conditions, we show that the extension is Frobenius, respectively separable, if and only if
S
is a Frobenius, respectively separable, algebra in the category of bimodules over
R
. In the case when
R
is separable we show that the extension is separable if and only if
S
is a separable algebra. Similarly, in the case when
R
is Frobenius and separable in a sovereign monoidal category we show that the extension is Frobenius if and only if
S
is a Frobenius algebra and the restriction at
R
of its Nakayama automorphism is equal to the Nakayama automorphism of
R
. As applications, we obtain several characterizations for an algebra extension associated to a wreath to be Frobenius, respectively separable.
European Mathematical Society - EMS - Publishing House GmbH
Title: On Frobenius and separable algebra extensions in monoidal categories: applications to wreaths
Description:
We characterize Frobenius and separable monoidal algebra extensions
i: R \to S
in terms given by
R
and
S
.
For instance, under some conditions, we show that the extension is Frobenius, respectively separable, if and only if
S
is a Frobenius, respectively separable, algebra in the category of bimodules over
R
.
In the case when
R
is separable we show that the extension is separable if and only if
S
is a separable algebra.
Similarly, in the case when
R
is Frobenius and separable in a sovereign monoidal category we show that the extension is Frobenius if and only if
S
is a Frobenius algebra and the restriction at
R
of its Nakayama automorphism is equal to the Nakayama automorphism of
R
.
As applications, we obtain several characterizations for an algebra extension associated to a wreath to be Frobenius, respectively separable.
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