Group partition categories

  title={Group partition categories},
  author={Samuel Nyobe Likeng and Alistair Savage},
  journal={Journal of Combinatorial Algebra},
To every group $G$ we associate a linear monoidal category $\mathcal{P}\mathit{ar}(G)$ 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 $\mathcal{P}\mathit{ar}(G)$ into the group Heisenberg category associated to $G$. This embedding intertwines the natural actions of both categories on modules for wreath products of $G$. Finally, we prove… 
2 Citations

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Jellyfish Partition Categories

  • J. Comes
  • Mathematics
    Algebras and Representation Theory
  • 2019
For each positive integer n , we introduce a monoidal category J P ( n ) $\mathcal {J}\mathcal {P}(n)$ using a generalization of partition diagrams. When the characteristic of the ground field is

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We introduce a notion of partition wreath product of a finite group by a partition quantum group, a construction motivated on the one hand by classical wreath products and on the other hand by the