Determinant and rank functions in semisimple pivotal Ab-categories
نویسندگان
1 Mathematical Sciences and Applications Laboratory, Department of Mathematics, Faculty of Sciences Dhar Al Mahraz, P. O. Box 1796, University Sidi Mohamed Ben Abdellah Fez, Morocco.
2 Mathematical Sciences and Applications Laboratory, Department of Mathematics, Faculty of Sciences Dhar Al Mahraz, P. O. Box 1796, University Sidi Mohamed Ben Abdellah Fez, Morocco.
3 Mathematical Sciences and Applications Laboratory, Department of Mathematics, Faculty of Sciences Dhar Al Mahraz, P. O. Box 1796, University Sidi Mohamed Ben Abdellah Fez, Morocco.
doi
10.48308/cgasa.19.1.47چکیده
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.
