Classification of Super-Modular Categories by Rank Academic Article

abstract

• 2019, Springer Nature B.V. We pursue a classification of low-rank super-modular categories parallel to that of modular categories. We classify all super-modular categories up to rank = 6, and spin modular categories up to rank = 11. In particular, we show that, up to fusion rules, there is exactly one non-split super-modular category of rank 2, 4 and 6, namely PSU(2) 4k+ 2 for k = 0,1 and 2. This classification is facilitated by adapting and extending well-known constraints from modular categories to super-modular categories, such as Verlinde and Frobenius-Schur indicator formulae.

authors

• Rowell, Eric

published proceedings

• ALGEBRAS AND REPRESENTATION THEORY

author list (cited authors)

• Bruillard, P., Galindo, C., Ng, S., Plavnik, J. Y., Rowell, E. C., & Wang, Z.

citation count

• 10

complete list of authors

• Bruillard, Paul||Galindo, Cesar||Ng, Siu-Hung||Plavnik, Julia Y||Rowell, Eric C||Wang, Zhenghan

publication date

• June 2020

publisher

• Springer Nature  Publisher

published in

• Algebras and Representation Theory  Journal

keywords

• Classification By Rank
• Fermionic Quotient
• Spin Modular Categories
• Super-modular Categories

Digital Object Identifier (DOI)

• 10.1007/s10468-019-09873-9

start page

• 795

end page

• 809

volume

• 23

issue

• 3

URL

• http://dx.doi.org/10.1007/s10468-019-09873-9