OFFSET

1,2

COMMENTS

A complex Grothendieck ring is a fusion ring admitting a categorification into a fusion category over the complex field.

See the comments in A348305 for the definition of fusion ring, rank, multiplicity.

A complex fusion category is a C-linear semisimple rigid tensor category with finitely many simple objects and finite dimensional spaces of morphisms, such that the neutral object is simple, see the book by Etingof-Gelaki-Nikshych-Ostrik mentioned below.

This counting comes from the paper by Liu-Palcoux-Ren mentioned below.

LINKS

P. Etingof, S. Gelaki, D. Nikshych and V. Ostrik, Tensor Categories, Mathematical Surveys and Monographs Volume 205 (2015).

Z. Liu, S. Palcoux and Y. Ren, Classification of Grothendieck rings of complex fusion categories of multiplicity one up to rank six, Lett Math Phys 112, 54 (2022); arXiv version, arXiv:2010.10264 [math.CT], 2020-2021.

EXAMPLE

For n=1, there is only the trivial one, so a(1)=1.

For n=2, there are only the cyclic group C2 one and the Yang-Lee one, so a(2)=2.

CROSSREFS

KEYWORD

nonn,hard,more

AUTHOR

Sébastien Palcoux, Mar 19 2022

STATUS

approved