%0 Journal Article
%T Determinant and rank functions in semisimple pivotal Ab-categories
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Draoui, Khalid
%A Choulli, Hanan
%A Mouanis, Hakima
%D 2023
%\ 08/01/2023
%V 19
%N 1
%P 47-80
%! Determinant and rank functions in semisimple pivotal Ab-categories
%K Monoidal category
%K strong tensor functor
%K quantum trace
%K McCoy rank
%K quantum determinants
%R 10.48308/cgasa.19.1.47
%X We investigate and generalize quantum determinants to semisimple spherical and pivotal categories. It is well known that traces are preserved by strong tensor functors; we show on one hand that in fact, weaker conditions on a functor are sufficient to continue preserving traces. On the other hand, we prove that these determinants are well-behaved under strong tensor functors. Further, we introduce a notion of domination rank for objects of a semisimple pivotal category and prove similar properties of the ordinary case. Furthermore, we expand the determinantal and McCoy ranks to introduce a morphism quantum rank function on a semisimple pivotal category.
%U https://cgasa.sbu.ac.ir/article_103829_ff81f70abc504501a6a6837d564fda92.pdf