To every group we associate a linear monoidal category that we call a group partition category. We give explicit bases for the morphism spaces and also an efficient presentation of the category in terms of generators and relations. We then define an embedding of into the group Heisenberg category associated to . This embedding intertwines the natural actions of both categories on modules for wreath products of . Finally, we prove that the additive Karoubi envelope of is equivalent to a wreath product interpolating category introduced by Knop, thereby giving a simple concrete description of that category.
Cite this article
Samuel Nyobe Likeng, Alistair Savage, Group partition categories. J. Comb. Algebra 5 (2021), no. 4, pp. 369–406DOI 10.4171/JCA/55