Euler totient of subfactor planar algebras
Operator Algebras
2018-03-30 v8 Combinatorics
Group Theory
Representation Theory
Abstract
We extend the Euler's totient function (from arithmetic) to any irreducible subfactor planar algebra, using the Mobius function of its biprojection lattice, as Hall did for the finite groups. We prove that if it is nonzero then there is a minimal 2-box projection generating the identity biprojection. We explain a relation with a problem of K.S. Brown. As an application, we define the dual Euler totient of a finite group and we show that if it is nonzero then the group admits a faithful irreducible complex representation. We also get an analogous result at depth 2, involving the central biprojection lattice.
Cite
@article{arxiv.1703.04486,
title = {Euler totient of subfactor planar algebras},
author = {Sebastien Palcoux},
journal= {arXiv preprint arXiv:1703.04486},
year = {2018}
}
Comments
11 pages. Accepted in Proc. Am. Math. Soc