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arXiv · 2007.00139

Representation dimensions linked by Frobenius bimodules with applications to group algebras

Changchang Xi
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Abstract

We establish relations between representation dimensions of two algebras connected by a Frobenius bimodule or extension. Consequently, upper bounds and equality formulas for representation dimensions of group algebras, symmetric separably equivalent algebras and crossed products are obtained. Particularly, for any subgroup H of a finite group G, if [G:H] is invertible in a field, then the representation dimensions of the group algebras of G and H over the field are the same.

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Changchang Xi. 2020-06-30. Representation dimensions linked by Frobenius bimodules with applications to group algebras. https://arxiv.org/abs/2007.00139

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