The Brauer-Picard group of the Asaeda-Haagerup fusion categories

Details The Brauer-Picard group of the Asaeda-Haagerup fusion categories The Brauer-Picard group of the Asaeda-Haagerup fusion categories

2012-02-20

arxiv.org/abs/1202.4396v1

Mathematics

Operator Algebras

49 pages, many figures

Scientific paper

We prove that the Brauer-Picard group of Morita autoequiv- alences of each of the three fusion categories which arise as an even part of the Asaeda-Haagerup subfactor or of its index 2 extension is the Klein four-group. We describe the 36 bimodule categories which occur in the full subgroupoid of the Brauer-Picard groupoid on these three fusion categories. We also classify all irreducible subfactors both of whose even parts are among these categories, of which there are 111 up to isomorphism of the planar algebra (76 up to duality). Although we identify the entire Brauer-Picard group, there may be additional fusion categories in the groupoid. We prove a partial classification of possible additional fusion categories Morita equivalent to the Asaeda-Haagerup fusion categories and make some conjectures about their existence; we hope to address these conjectures in future work.

Affiliated with

Also associated with

No associations

Rating

The Brauer-Picard group of the Asaeda-Haagerup fusion categories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Brauer-Picard group of the Asaeda-Haagerup fusion categories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Brauer-Picard group of the Asaeda-Haagerup fusion categories will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-565579